Question

triangle pqr is similar to triangle wyx.
if the length of \\(\overline{wx} = 5.0\\), what is the length of \\(\overline{pr}\\)?
(options: a) 10.5 inches, b) 9.33333333333 inches, c) 7.5 inches, d) 2.5 inches)

Explanation:

Step1: Determine the ratio of similarity

Since \(\triangle PQR\sim\triangle VWX\), the ratio of corresponding sides is equal. The ratio of \(WQ\) to \(WX\) is \(\frac{19.5}{13}\).

Step2: Calculate the length of \(PR\)

Let \(PR = x\). Using the ratio of similarity \(\frac{PR}{VX}=\frac{QR}{WX}\). Substitute \(QR = 7.5\), \(WX = 5\) and the ratio \(\frac{19.5}{13}= 1.5\). We have \(x=\frac{7.5\times13}{5}\).

$$x=\frac{97.5}{5}=19.5$$

Answer:

\(19.5\) inches