Question

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

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. Let \( FG = x \). We have the proportion \(\frac{BC}{CD}=\frac{EF}{FG}\). Substituting the known values: \(BC = 8\), \(CD=17\), \(EF = 31\). So the equation is \(\frac{8}{17}=\frac{31}{x}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(8x=17\times31\). Calculate \(17\times31 = 527\). Then \(x=\frac{527}{8}\).

Step3: Calculate the value of \(x\)

\(x=\frac{527}{8}=65.875\approx65.9\)

Answer:

\(65.9\)