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: Identify corresponding sides

Since $\triangle CDE \sim \triangle FGH$, the corresponding sides are proportional. Side $CE$ (length 13) in $\triangle CDE$ corresponds to side $FH$ (length 47) in $\triangle FGH$, and side $CD$ (length 6) in $\triangle CDE$ corresponds to side $FG$ (let's call it $x$) in $\triangle FGH$. So the proportion is $\frac{CE}{FH} = \frac{CD}{FG}$.

Step2: Set up the proportion

Substitute the known values: $\frac{13}{47} = \frac{6}{x}$.

Step3: Solve for $x$

Cross - multiply: $13x = 47\times6$. Then $13x = 282$. Divide both sides by 13: $x=\frac{282}{13}\approx21.7$.

Answer:

21.7