Question

triangle cde is similar to triangle fgh. find the measure of side fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since \(\triangle CDE \sim \triangle FGH\), the corresponding sides are proportional. Let's assume \(CD\) corresponds to \(FG\) and \(DE\) corresponds to \(GH\). So, \(CD = 16\), \(DE = 33\), \(GH = 8\), and we need to find \(FG\).

Step2: Set up proportion

The proportion for similar triangles is \(\frac{CD}{FG}=\frac{DE}{GH}\). Substituting the known values: \(\frac{16}{FG}=\frac{33}{8}\).

Step3: Solve for \(FG\)

Cross - multiply: \(33\times FG=16\times8\). Then \(33FG = 128\). So, \(FG=\frac{128}{33}\approx3.9\) (rounded to the nearest tenth).

Answer:

\(3.9\)