Question

question
triangle ghi is similar to triangle jkl. find the measure of side jk. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since \(\triangle GHI \sim \triangle JKL\), the ratios of corresponding sides are equal. Let's assume \(GI\) corresponds to \(JL\) and \(GH\) corresponds to \(JK\). So, \(\frac{GI}{JL}=\frac{GH}{JK}\).
We know \(GI = 8\), \(JL = 31\), and \(GH = 13\). Let \(JK = x\).

Step2: Set up proportion

\(\frac{8}{31}=\frac{13}{x}\)

Step3: Solve for \(x\)

Cross - multiply: \(8x=13\times31\)
\(8x = 403\)
\(x=\frac{403}{8}=50.375\approx50.4\)

Answer:

\(50.4\)