Tom wants to put up Christmas lights around his house.
His house is a rectangle which is 35 m long and 15 m wide.

Tom will need
metres of lights to go all the way around his house.

The total area of the pool and the walkway will be 210 square feet, the walkway should be 1.8 feet wide.

In mathematics, area is a measure of the size or extent of a two-dimensional shape or surface. It is typically measured in square units, such as square meters, square feet, or square inches. The area of a shape is calculated by multiplying its length by its width or by using a formula specific to that shape.

The concept of area is fundamental to many areas of mathematics, science, and engineering. It is used to calculate the size of land and buildings in real estate, the amount of material needed for construction, the amount of paint needed to cover a surface, and many other practical applications. In addition, the study of area is important in geometry, calculus, and other areas of mathematics.

Let's start by finding the area of the pool, which is 9 feet by 8 feet:

Area of pool = 9 feet * 8 feet = 72 square feet

Next, we need to add the width of the walkway to each dimension of the pool to find the dimensions of the entire area:

Width of area = 9 feet + 2(width of walkway)

Length of area = 8 feet + 2(width of walkway)

The total area of the pool and walkway is given as 210 square feet, so we can set up the equation:

Area of pool + Area of walkway = 210 square feet

Substituting the formulas for the area of the pool and area of the walkway, we get:

72 + (9 + 2x)(8 + 2x) = 210

Expanding the right side and simplifying, we get:

4x² + 34x - 33 = 0

We can solve for x using the quadratic formula:

x = (-34 ± √(34² - 44(-33))) / (2*4)

x = (-34 ± √(1660)) / 8

x = (-34 ± 40.74) / 8

x = 1.8 or x = -5.075

Since the width of the walkway cannot be negative, the width of the walkway should be 1.8 feet.

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To find out how long it would take to turn a $13,000 investment in Japan into $16,000 with annual compound interest, the formula for compound interest can be used. By solving for t, we can find that it would take about 2.72 years, assuming an interest rate of 7.97%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)⁽ⁿᵗ⁾

where:

A = the final amount

P = the initial investment

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we are given that P = $13,000, A = $16,000, r is not given, n = 1 (since the interest is compounded annually), and we want to solve for t.

First, we can rearrange the formula to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we get:

t = (log(16000/13000)) / (1 * log(1 + r/1))

Simplifying the equation gives:

t = log(1.2308) / log(1 + r)

To solve for t, we need to know the annual interest rate, r. We can rearrange the formula for compound interest to solve for r:

r = n[(A/P)⁽¹/⁽¹*ᵗ⁾⁾ - 1]

Substituting the given values, we get:

r = 1[(16000/13000)⁽¹/⁽¹*ᵗ⁾⁾ - 1]

Simplifying the equation gives:

r = (16000/13000)⁽¹/ᵗ⁾ - 1

We can then use trial and error or a calculator to solve for t. One way is to plug in different values for t until we get an r that makes sense. For example:

If we assume t = 3 years, then:

r = (16000/13000)⁽¹/³⁾ - 1

r = 0.0797

Plugging this value of r back into the equation for t gives:

t = log(1.2308) / log(1 + 0.0797)

t ≈ 2.72 years

Therefore, if you invest $13,000 in Japan and the interest is compounded annually, you would need to wait approximately 2.72 years for your investment to be worth $16,000.

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The speed of the train is 40 km/h. and the length and breadth of the plot are 33 meters and 16 meters respectively.

The solution is as follows :-

(i) Let's assume that the breadth of the rectangular plot is x meters. Then, according to the problem, the length of the plot is (2x + 1) meters. The area of the plot is given as 528 m². We know that the area of a rectangle is given by the product of its length and breadth. So we can write:

Area = length x breadth

528 = (2x + 1) x x

Simplifying this equation, we get:

528 = 2x² + x

2x² + x - 528 = 0

This is a quadratic equation in the variable x. We can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 1, and c = -528. Plugging in these values, we get:

x = (-1 ± √(1² - 4(2)(-528))) / 2(2)

x = (-1 ± √(1 + 4224)) / 4

x = (-1 ± 65) / 4

The negative value of x does not make sense in the context of the problem. So we can discard it and take the positive value of x:

x = 16

This means that the breadth of the plot is 16 meters. The length of the plot is given as (2x + 1), which evaluates to 33 meters.

So the length and breadth of the plot are 33 meters and 16 meters respectively.

(ii) Let's assume that the speed of the train is x km/h. According to the problem, the distance traveled by the train is 480 km. We know that speed is defined as distance traveled per unit time. So the time taken by the train to cover the distance of 480 km at a speed of x km/h is given by:

time = distance / speed

time = 480 / x

If the speed of the train had been 8 km/h less, the time taken to cover the same distance would have been 3 hours more. So we can write another equation for the time taken in this case:

time + 3 = 480 / (x - 8)

Now we can set these two equations equal to each other, since they both represent the time taken to cover the same distance:

480 / x = 480 / (x - 8) + 3

Simplifying this equation, we get:

480(x - 8) = 480x + 3x(x - 8)

480x - 3840 = 480x + 3x² - 24x

3x² - 24x - 3840 = 0

Dividing both sides by 3, we get:

x² - 8x - 1280 = 0

This is a quadratic equation in the variable x. We can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -8, and c = -1280. Plugging in these values, we get:

x = (8 ± √(64 + 5120)) / 2

x = (8 ± √5184) / 2

x = (8 ± 72) / 2

The negative value of x does not make sense in the context of the problem. So we can discard it and take the positive value of x:

x = 40

Therefore, the speed of the train is 40 km/h.

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Answer:

$39.60

Step-by-step explanation:

10% of 36 is 3.6

36 + 3.6 = 39.6

If the amount of time is exponentially distributed with mean 20 minutes, then the standard deviation of the time a student would spend at a terminal is also 20 minutes.

The amount of time which the student spends at a terminal in ISEN computer-room is said to be exponentially distributed, and

The mean-time spent at computer room is = 20 minutes,

We know that, for an exponentially-distributed random variable, the standard deviation is equal to the mean.

So, the standard deviation of the time a student spends at a terminal is also 20 minutes, since the mean is given as 20 minutes.

Therefore, the standard deviation is 20 minutes.

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Answer: y = 101
z = 68

Step-by-step explanation:

Z first, bcs its ez
180 - 112 (angles on a straight line)
z = 68

104 + 87 + 68 + y = 360 (angles in a quadrilateral)
360 - 104 + 87 + 68 = y
360 - 259 = y
y = 101

As a result, each small basket contain X=8 pieces of fruit and each large basket contains Y=17.

There are numerous practical uses for algebra. Among the most frequent applications of algebra are:

- Seeing a ball game being played by 4-5 year old children.

- Creating an activity schedule

- Cooking or doubling or splitting the dish; - Improving spatial intelligence; - Determining tax liability; - Calculating the stars

- Advances in technology - Budgeting

Assume that each small basket contains x pieces of fruit and each large basket contains y pieces of fruit.

We can create two equations using the information provided:

3x + 5y = 109

9x + 5y = 157

When the first equation is subtracted from the second equation, the result is: 6x = 48

x = 8.

Any of the two equations can be solved for x = 8 and the result is:

3(8) + 5y = 109

24 + 5y = 109

5y = 85

y = 17

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The equivalent measurements are 0.76 grams = 0.076 decagrams as 1gram = 0.1 decagrams. Option A is correct answer.

What is Measurement?

Measurement is the process of associating numbers with physical quantities and phenomena. Measurement is fundamental to the sciences; to engineering, construction, and other technical fields; and to almost all everyday activities. For that reason the elements, conditions, limitations, and theoretical foundations of measurement have been much studied. See also measurement system for a comparison of different systems and the history of their development.

Measurements may be made by unaided human senses, in which case they are often called estimates, or, more commonly, by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly sophisticated systems designed to detect and measure quantities entirely beyond the capabilities of the senses, such as radio waves from a distant star or the magnetic moment of a subatomic particle.

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For the given problem, the null hypothesis cannot be tested because the sample is less than 30 boxes of cereal package filling is b)false.

The size of the sample does not affect the ability to test a null hypothesis. The sample size can affect the statistical power of the test (i.e., the ability to detect a true difference if it exists), but it does not affect the ability to test the null hypothesis itself.

There are statistical tests, such as the t-test and the z-test, that can be used to test hypotheses even with small sample sizes. Alternatively, non-parametric tests can also be used when the assumptions of the parametric tests are not met.

In statistics, the null hypothesis is a statement that there is no significant difference or relationship between two or more variables, or that any observed difference or relationship is due to chance or random sampling variability.

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The standard form of the equation of the hyperbola is 49y² - 2401x² = 2401.

Standard form of an equation is a specific format in which an equation is written. In the context of mathematics, there are several types of standard forms depending on the type of equation.

The standard form of the equation of a hyperbola with center at the origin, vertices on the y-axis, and horizontal asymptotes is given by:

(y / b)² - (x / a)² = 1

where a is the distance from the center to each vertex along the x-axis and b is the distance from the center to each point where the hyperbola intersects the y-axis.

From the given information, we can see that the center of the hyperbola is at the origin and the distance from the center to each vertex on the y-axis is 7. Therefore, b = 7.

To find a, we can use the fact that the slope of the asymptotes is ±b/a. We are given the equation of asymptotes as y = ±(7/4)x. Comparing this to the standard form of the equation of the asymptotes (y = ±(b/a)x), we can see that b/a = 7/4. Solving for a, we get:

a = b / (4/7) = 7(7/4) = 49/4

Substituting these values into the standard form of the equation of a hyperbola, we get:

(y / 7)² - (x / (49/4))² = 1

Multiplying both sides by (49/4)², we can rewrite the equation in standard form:

49y² - 2401x² = 2401

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1) For A Plus Plumbing

A. The cost per hour of work is $60 per hour.

B. The one-time fee is $320.

2) For Quality Plumbing:

The cost for x hours of work is given by the equation cost = 50x - 50

1) For A Plus Plumbing:

A. To calculate the cost per hour of work, we need to find the slope of the line connecting two points on the table. Let's use the first two rows:

slope = (cost2 - cost1) / (time2 - time1) = (140 - 80) / (2 - 1) = 60

So the cost per hour of work for A Plus Plumbing is $60 per hour.

B. The one-time fee is given in the table as the cost when time is zero. From the table, we can see that the one-time fee for A Plus Plumbing is $320.

2) For Quality Plumbing,

We can see from the graph that the cost starts at $50 for two hours of work and increases by $50 for each additional hour. This means that the cost for x hours of work can be calculated using the equation:

cost = 50 + 50(x-2) = 50x - 50

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The given question is incomplete, the complete question is:

Two plumbing companies charge money for each hour of work, plus a one-time fee. A Plus Plumbing charges according to this table: time (hours) cost (dollars) row 10 80 row 21 140 row 3 4 320 Quality Plumbing charges according to this graph 2501 200 cost (dollars) 150 100 50 2 3 4 5 6 time (hours) 1. For A Plus Plumbing A. How much does it cost for each hour of work? B. What is the one-time fee? 2. For Quality Plumbing A. How much do they charge for each hour of work?

The value of imports is $304,533,333.33 and the value of exports is $311,633,333.33. So, option B is correct.

Let's denote the value of exports as E and the value of imports as I. We can then use the following system of equations to solve for E and I:

E - I = 7,100,000 (balance of trade equation)

0.12E + 0.21I = 9,148,200 (tariff revenue equation)

Multiplying the first equation by 0.12 and adding it to the second equation, we get:

0.12E - 0.12I + 0.21I = 9,148,200 + 0.12(7,100,000)

0.12E + 0.09I = 9,988,000

Multiplying both sides by 100, we can eliminate decimals:

12E + 9I = 998,800,000

We can now use this equation with the balance of trade equation to solve for E and I:

E - I = 7,100,000

12E + 9I = 998,800,000

Multiplying the first equation by 9 and subtracting it from the second equation, we get:

12E + 9I - 9E + 9I = 998,800,000 - 63,900,000

3E = 934,900,000

E = 311,633,333.33

Substituting this value into the balance of trade equation, we get:

311,633,333.33 - I = 7,100,000

I = 304,533,333.33

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To compare the means of two distinct groups where one group receives a manipulation and the other serves as the control group, you will run an Independent Samples t-test. This statistical test is used to determine if there is a significant difference between the means of two independent groups on a given measure.

Here's a step-by-step explanation:

1. Define your null hypothesis (H0) and alternative hypothesis (H1). The null hypothesis usually states that there is no significant difference between the means, while the alternative hypothesis states that there is a significant difference.

2. Determine the level of significance (alpha) for the test, typically set at 0.05 or 0.01.

3. Collect data from both groups and calculate their respective means and standard deviations.

4. Calculate the t-value using the formula:
t = (M1 - M2) / sqrt((SD1^2 / n1) + (SD2^2 / n2))
where M1 and M2 are the means, SD1 and SD2 are the standard deviations, and n1 and n2 are the sample sizes of the two groups.

5. Determine the degrees of freedom (df) for the test using the formula:
df = n1 + n2 - 2

6. Use the t-value and degrees of freedom to find the corresponding p-value in a t-distribution table or by using statistical software.

7. Compare the p-value to the predetermined level of significance (alpha). If the p-value is less than or equal to the alpha, you can reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.

In summary, to compare the means of two distinct groups with different manipulations, you should perform an Independent Samples t-test. This test helps you determine whether the observed differences between the groups are statistically significant or due to random chance.

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The value of k is equal to one half in the given case.

Since g(x) = f(kx), the value of k can be found by comparing the input values of g(x) to the corresponding input values of f(x) when x is multiplied by k.

Let's compare the values of g(x) and f(x) for x = -2:

g(-2) = 4, which means f(k(-2)) = 4, or f(-2k) = 4

f(-2) = 4, which means -2k is one of the inputs for f(x) that gives an output of 4

Next, let's compare the values of g(x) and f(x) for x = 2:

g(2) = 4, which means f(k(2)) = 4, or f(2k) = 4

f(2) = 4, which means 2k is one of the inputs for f(x) that gives an output of 4

We now have two equations: -2k is an input for f(x) that gives an output of 4, and 2k is also an input for f(x) that gives an output of 4. Therefore, we can solve for k by setting the two equations equal to each other and solving for k:

-2k = 2k/2

Multiplying both sides by -1/2, we get:

k = 1/2

Therefore, the value of k is equal to one half.

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In the above mentioned similar triangles the length of DE is 5.25 cm.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Since triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to set up a proportion:

AB / AD = BC / DE

Substituting the given values, we get:

8 / AD = 6 / DE

Multiplying both sides by DE, we get:

8DE / AD = 6

Dividing both sides by 8/AD, we get:

DE = (6/8)AD

We need to find AD to solve for DE. To do this, we can use the fact that BD is an altitude of triangle ABC and triangle ADE is similar to triangle ABC. Therefore, triangle ABD is also similar to triangle ABC, and we can set up another proportion:

BD / AB = AD / AC

Substituting the given values, we get:

4 / 8 = AD / (8 + 6)

Simplifying, we get:

1/2 = AD / 14

Multiplying both sides by 14, we get:

AD = 7

Substituting this value back into the first equation, we get:

DE = (6/8)AD = (6/8)7 = 21/4 = 5.25

Therefore, the length of DE is 5.25 cm.

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Answer: x=13

y=9

Step-by-step explanation:

yw dawg

Answer:

y=2x-13

Step-by-step explanation:

The wrong reporting on the survey represented by study uses statistical method is given by option A. The conclusion is based on a correlation that implies causality.

The problem with reporting the results of the survey as 'adding weight to a car is what makes it consume more fuel'.

It implies causality based solely on the observed correlation between car weight and fuel consumption.

Correlation does not imply causation.

Meaning that the fact that two variables are correlated does not necessarily mean that one causes the other.

It is possible that there is a third variable that causes both car weight and fuel consumption to increase.

Or that the correlation is purely coincidental.

It is important to be cautious about interpreting correlation as causation.

And based on statistical methods consider other possible explanations for the observed relationship between the variables.

Therefore, correct answer based on study of statistical methods is option A.  conclusion is based on a correlation that implies causality.

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The above question is incomplete, the complete question is:

A study uses statistical methods to conclude that there is an association between the weights of cars and the amounts of fuel consumption. The study then concludes that adding weight to a car is what makes it consume more fuel. What is wrong with reporting the results of the survey this way?

A)The conclusion is based on a correlation that implies causality.

B)The conclusion is based on a small sample.

C)The conclusion is based on a voluntary response sample.

D)The conclusion is based on a bad sample.

The steps involved in finding the standard deviation are finding mean, then calculating the square of difference, adding all and dividing by observations and at last the square root.

What is standard deviation?

The standard deviation assesses how widely distributed the data are relative to the mean.

We know that the standard deviation formula is represented as

√Σ[tex]{\frac{|x - mean|^{2} }{N} }[/tex]

The various steps undertaken are:

Step 1 : We are required to calculate the mean of the data by dividing the sum with the number of observations.

Step 2 : We subtract each observation from the mean and find the square.

Step 3 : All the values obtained in the previous step are added.

Step 4 : The value so obtained is divided by the number of observations.

Step 5 : This is the last step wherein the square root of the value obtained in the previous step is to be calculated.

Hence, these are the steps for finding the standard deviation.

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The value of X in the bottom question is 3.

The MidSegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

To solve for X in the top and bottom questions using the MidSegment theorem, we need to first identify the midpoints of the two sides and the third side.

For the top question, we can see that the midpoints of AB and BC are D and E respectively. So, DE is parallel to AC and half its length. We know that AC = 12, so DE = 6. We also know that DE = X + 1, so we can set up an equation:

X + 1 = 6

Solving for X, we get:

X = 5

Therefore, the value of X in the top question is 5.

For the bottom question, we can see that the midpoints of AB and AC are D and F respectively. So, DF is parallel to BC and half its length. We know that BC = 14, so DF = 7. We also know that DF = X + 4, so we can set up an equation:

X + 4 = 7

Solving for X, we get:

X = 3

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Answer:

≈ 9144 ft^2

Step-by-step explanation:

Given:

H = 30 ft

d = 52 ft

π = 3,14

Find: A (surface) - ?

First, let's find the radius:

r = 0,5 × d

r = 0,5 × 52 = 26 ft

Now, we can find the surface area of the cylinder ( the cylinder's surface area contains 2 circle bases and a lateral surface):

[tex]a(surface) = 2\pi {r}^{2} + 2\pi \times r \times h[/tex]

[tex]a(surface) = 2 \times 3.14 \times {26}^{2} + 2 \times 3.14 \times 26 \times 30 ≈9144 \: {ft}^{2} [/tex]

According to the question the length of the real airplane is 63 feet and the wingspan of the airplane in the scale drawing is 10 inches.

If 1 inch in the scale drawing represents 9 feet in the real airplane, then 7 inches in the scale drawing represents:

7 inches x 9 feet/inch = 63 feet

So, the length of the real airplane is 63 feet.

(b) If 1 inch in the scale drawing represents 9 feet in the real airplane, then X inches in the scale drawing represents 90 feet in the real airplane. We can construct a ratio to find the value of X:

1 inch / 9 feet = X inches / 90 feet

Cross-multiplying, we get:

9 feet * X inches = 1 inch * 90 feet

Simplifying, we get:

X inches = 10 inches

As a result, the scale drawing's scale model's airplane has a 10 inch wingspan.

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There is no value of x that meets the requirements because this is a contradiction.

The angle addition postulate can be used to determine the value of x. According to the angle addition postulate, if point Y is inside the angle ZUVX, then

According to the geometry postulate known as the angle addition, if two or more angles are placed side by side, with a common vertex and arm connecting each pair, the sum of those angles will equal the sum of the resulting angle1.

Take the two nearby angles ACB and CDB as an illustration. To identify undiscovered angles, we can combine their measurements. According to the angle addition postulate,∠ ACB + ∠CDB equals∠ ADC2.

ZUVX plus YUVX equals ZVYX and YVYX.

Since mVYX = 282 and mZUVX = (4x - 5) are known values, we may replace them in the equation as follows:

(4x - 5) + mYUVX + mZVYX = 282

The values of mYUVX and mZVYX are unknown, but since they are supplementary angles, we do know that they add up to 180 degrees. Hence, we may replace mYUVX with 180 - mZUVX and mZVYX with 180 - mVYX:

(180 - mZUVX) + (4x - 5) = 282 + (180 - mVYX)

When we simplify this equation, we obtain:

4x - 5 + 180 - (4x - 5) = 282 + 180 - 282

More simplification results in:

175 = 78

No value of x is there:

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Therefore, if the test statistic falls in the critical region, we select option (b) - reject the null and conclude that there is strong support for the research hypothesis.

What happens if the test statistic falls in the critical region?

If the test statistic falls in the critical region, we reject the null and conclude that there is strong support for the research hypothesis.

A critical region is the set of all values of the test statistic that lead to the rejection of the null hypothesis. It is a predefined set of values in which the alternative hypothesis will be favored if the sample test statistic falls within that range.

The critical region is that area in which the null hypothesis is rejected at a certain significance level. If the test statistic falls into the critical region, we can reject the null hypothesis in favor of the alternative hypothesis.

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The formula you will need in order to solve this question is [tex]2(wl+hl+hw)[/tex]

Step 1: Consider the information that has been provided to you in the problem.

W = 4

L = 8

H = 6

Step 2: Substitute the width, length, and height into the formula provided.

2(4×8+6×8+6×4)

Step 3: Solve.

2(4×8+6×8+6×4) = 208

With that being said, the answer to your question is 208 cm.

The value of LJ is 18 feet where GH is 36ft and KP equal to PL.

The same angles, and the corresponding sides are proportional to each other. In other words, if you were to enlarge or reduce one of the triangles, it would still have the same angles as the other triangle.

If we create a dotted line connecting H and P as well as J and P,

∠JLP = ∠HKP (Similarity of triangles)

For example, consider two triangles ABC and DEF. If angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F, then the triangles are similar. If, in addition, the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, and also equal to the ratio of the length of side AC to side DF, then the triangles are not only similar, but they are also in proportion.

HP = JP

KP = LP

ΔHKP ≅ ΔJLP

KH = LJ

Now joining G and P,

GP = HP

PM is parallel to the GH.

PM divides GH evenly.

KH = GK = 1/2 of GH.

= 1/2 × 36

= 18 feet

As a result, we may say that LJ is 18 feet long.

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