Question

triangle efg is similar to triangle hij. find the measure of side hi. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle EFG\sim\triangle HIJ\), the ratios of corresponding sides are equal. Let \(HI = x\). The proportion is \(\frac{EF}{HI}=\frac{EG}{HJ}\). Here, \(EF = 3\), \(EG = 5\), and \(HJ=24\). So the proportion becomes \(\frac{3}{x}=\frac{5}{24}\).

Step2: Cross - multiply

Cross - multiplying gives \(5x=3\times24\).

Step3: Solve for \(x\)

First, calculate \(3\times24 = 72\). Then, \(x=\frac{72}{5}=14.4\).

Answer:

\(14.4\)