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#RS

[tex]\\ \rm\Rrightarrow \dfrac{RS}{TS}=\dfrac{FG}{EF}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{RS}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow RS=\dfrac{12(5)}{2}=6(5)=30[/tex]

#QR

[tex]\\ \rm\Rrightarrow \dfrac{HG}{EF}=\dfrac{QR}{TS}[/tex]

[tex]\\ \rm\Rrightarrow QR=TS=12[/tex]

#QU

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{QR}=\dfrac{DH}{HG}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow UQ=30[/tex]

Answer:

RS = 30, QR = 12, QU = 30

Step-by-step explanation:

Step 1:  Determine RS

We can see that RS on the left shape corresponds to FG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of RS.  We can also see that the shape has been flipped so EF would match to ST.

[tex]RS/ST = FG/EF[/tex]

[tex]RS/12 = 45/18[/tex]

[tex]RS * 18 = 12 * 45[/tex]

[tex]\frac{18*RS}{18} = 540 / 18[/tex]

[tex]RS = 30[/tex]

Step 2:  Determine QR

We can see that QR on the left shape corresponds to HG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QR.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QR/ST = HG/EF[/tex]

[tex]QR/12 = 18/18[/tex]

[tex]QR * 18 = 12 * 18[/tex]

[tex]\frac{18 * QR}{18} = 216 / 18[/tex]

[tex]QR = 12[/tex]

Step 3:  Determine QU

We can see that QR on the left shape corresponds to DH on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QU.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QU/ST = DH/EF[/tex]

[tex]QU/12 = 45/18[/tex]

[tex]QU * 18 = 12 * 45[/tex]

[tex]\frac{18*QU}{18} = 540/18[/tex]

[tex]QU = 30[/tex]

Answer:  RS = 30, QR = 12, QU = 30

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