Question

Given: APQR VAXYZ. What is the length of side PR? (T.G.7)(1 point) Y 9 5 Х N P 2x - 4 R O A. 25 O B. 36 O C. 20 O D 40

Answer 1

If the triangles are similar then the ratio between corresponding sides remains constant:

$\frac{PQ}{XY}=\frac{QR}{YZ}=\frac{PR}{XZ}$

We have

• PQ = 9

,

• XY = 5

,

• PR = 2x-4

,

• XZ = x

We can find x with the ratio:

$\begin{gathered} \frac{PQ}{XY}=\frac{PR}{XZ} \\ \frac{9}{5}=\frac{2x-4}{x} \end{gathered}$$\begin{gathered} 9x=5(2x-4) \\ 9x=10x-20 \\ 20=10x-9x \\ 20=x \end{gathered}$

If x = 20, then

$PR=2x-4=2\cdot20-4=36$

PR = 36