Question

3 triangle pqr is similar to triangle vwx.
if the length of \\( \overline{vx} \\) is 5.0, what is the length of \\( \overline{pr} \\)?
(options are partially visible but include multiple choice format)

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is equal. Let's find the ratio of \(PQ\) to \(VW\).
\(\frac{PQ}{VW}=\frac{19.5}{13}\)
\(=\frac{19.5\div6.5}{13\div6.5}=\frac{3}{2}\)

Step2: Use the scale factor to find \(PR\)

We know that \(\frac{QR}{WX}=\frac{PR}{VX}\). We have \(QR = 7.5\) in, \(WX = 5\) in. Let \(PR=x\) and \(VX = 5.0\) in.
Since the scale factor \(\frac{3}{2}\), and \(\frac{QR}{WX}=\frac{7.5}{5}=\frac{3}{2}\)
So \(\frac{PR}{VX}=\frac{3}{2}\), substituting \(VX = 5.0\)
\(x=\frac{3}{2}\times5.0\)
\(x = 7.5\)

Answer:

\(7.5\) inches