Question

triangle cde is similar to triangle fgh. find the measure of side gh. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the side corresponding to $CD = 6$ in $\triangle FGH$ be $FG = 50.4$, and the side corresponding to $DE=4$ in $\triangle FGH$ be $GH$. The proportion is $\frac{CD}{FG}=\frac{DE}{GH}$.

Step2: Substitute values

Substitute $CD = 6$, $FG = 50.4$, and $DE = 4$ into the proportion: $\frac{6}{50.4}=\frac{4}{GH}$.

Step3: Cross - multiply

Cross - multiplying gives $6\times GH=4\times50.4$.

Step4: Solve for $GH$

First, calculate $4\times50.4 = 201.6$. Then, $GH=\frac{201.6}{6}=33.6$.

Answer:

$33.6$