Question

in the diagram below, \\( \triangle ief \sim \triangle ghf \\). find \\( q \\).

write your answer as a whole number or a decimal. do not round.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle IEF\sim\triangle GHF\), the ratios of corresponding sides are equal. That is \(\frac{q}{15.3}=\frac{9}{13.5}\)

Step2: Solve for \(q\)

Cross - multiply: \(13.5q = 15.3\times9\)

First, calculate \(15.3\times9=137.7\)

Then, \(q=\frac{137.7}{13.5}\)

\(q = 10.2\)

Answer:

\(10.2\)