Question

triangle efg is similar to triangle hij. find the measure of side ij. 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 \(IJ = x\). The proportion is \(\frac{FG}{IJ}=\frac{EF}{HI}\). Here \(FG = 8\), \(EF = 6\), \(HI=31.5\). So \(\frac{8}{x}=\frac{6}{31.5}\).

Step2: Cross - multiply

Cross - multiplying gives \(6x=8\times31.5\).

Step3: Solve for \(x\)

First, calculate \(8\times31.5 = 252\). Then \(x=\frac{252}{6}\).

Answer:

\(42\)