Question

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

Explanation:

Step1: Set up the proportion

Since \(\triangle CDE\sim\triangle FGH\), the ratios of corresponding sides are equal. Let \(GH = x\). Then \(\frac{CD}{FG}=\frac{DE}{GH}\). Substituting the given values: \(\frac{5}{18.3}=\frac{10}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(5x=18.3\times10\).

Step3: Solve for \(x\)

\(5x = 183\), so \(x=\frac{183}{5}=36.6\).

Answer:

\(36.6\)