Question

triangle def is similar to triangle ghi. find the measure of side gh. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle DEF\sim\triangle GHI\), the ratios of corresponding sides are equal. Let \(GH = x\). The proportion is \(\frac{DF}{GI}=\frac{DE}{GH}\). Substituting the values \(DF = 2\), \(GI=6.4\), \(DE = 3\) into the proportion: \(\frac{2}{6.4}=\frac{3}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(2x=3\times6.4\).

Step3: Solve for \(x\)

First, calculate \(3\times6.4 = 19.2\). Then, \(x=\frac{19.2}{2}\).

Answer:

\(9.6\)