Question

triangle cde is similar to triangle fgh. find the measure of side gh. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since \(\triangle CDE\sim\triangle FGH\), the ratios of corresponding sides are equal. Let \(GH = x\). The proportion is \(\frac{DE}{GH}=\frac{CD}{FG}\). Substituting the values \(DE = 10\), \(CD = 13\), \(FG=53\), we get \(\frac{10}{x}=\frac{13}{53}\).

Step2: Cross - multiply

Cross - multiplying gives \(13x=10\times53\). So, \(13x = 530\).

Step3: Solve for \(x\)

Divide both sides by \(13\): \(x=\frac{530}{13}\approx40.8\).

Answer:

\(40.8\)