Question

quadrilateral bcde is similar to quadrilateral fghl. find the measure of side gh. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let the length of $GH$ be $x$. We have the proportion $\frac{BC}{FG}=\frac{CD}{GH}$. Given $BC = 8$, $FG=40$, and $CD = 13.5$. So, $\frac{8}{40}=\frac{13.5}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $8x=40\times13.5$.

Step3: Solve for x

First, calculate $40\times13.5 = 540$. Then, $x=\frac{540}{8}=67.5$.

Answer:

$67.5$