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 $GH = x$. The ratio of the corresponding sides is $\frac{BC}{FG}=\frac{CD}{GH}$. We know $BC = 8$, $FG = 40$, and $CD = 135$. So the proportion is $\frac{8}{40}=\frac{135}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $8x=40\times135$.

Step3: Solve for x

First, calculate $40\times135 = 5400$. Then, $x=\frac{5400}{8}=675$.

Answer:

$675$