Question

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

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle CDE\sim\triangle FGH\), the ratios of corresponding sides are equal. That is \(\frac{CE}{FH}=\frac{CD}{FG}\).
We know \(CE = 13\), \(FH=47\), \(CD = 6\), and we need to find \(FG\).

Step2: Substitute the values into the proportion

Substituting the values into \(\frac{CE}{FH}=\frac{CD}{FG}\), we get \(\frac{13}{47}=\frac{6}{FG}\).
Cross - multiply: \(13\times FG=47\times6\).
So \(13FG = 282\).

Step3: Solve for \(FG\)

Divide both sides by 13: \(FG=\frac{282}{13}\approx21.7\).

Answer:

\(FG\approx21.7\)