Question

question
triangle cde is similar to triangle fgh. find the measure of side fg. round your answer to the nearest tenth if necessary.
e 14 d
h 57 g
c 23
f

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle CDE \sim \triangle FGH\), the sides \(DE\) and \(GH\) are corresponding, and \(CD\) and \(FG\) are corresponding. So, \(\frac{DE}{GH}=\frac{CD}{FG}\).

Step2: Substitute Known Values

We know \(DE = 14\), \(GH = 57\), and \(CD = 23\). Substituting these into the proportion: \(\frac{14}{57}=\frac{23}{FG}\).

Step3: Solve for \(FG\)

Cross - multiply: \(14\times FG=57\times23\). Calculate \(57\times23 = 1311\). Then, \(FG=\frac{1311}{14}\approx93.6\).

Answer:

\(93.6\)