Question

triangle ghi is similar to triangle jkl. find the measure of side lj. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since \(\triangle GHI\sim\triangle JKL\), the ratios of corresponding sides are equal. Let \(LJ = x\). The proportion is \(\frac{I G}{LJ}=\frac{I H}{L K}\). Substituting the given values: \(\frac{14}{x}=\frac{19}{59}\).

Step2: Cross - multiply

Cross - multiplying gives \(19x=14\times59\).

Step3: Solve for \(x\)

First, calculate \(14\times59 = 826\). Then \(x=\frac{826}{19}\approx43.5\).

Answer:

\(43.5\)