Question

quadrilateral f g h i is similar to quadrilateral j k l m. find the measure of side k l. 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 ratio of corresponding sides be $\frac{FG}{JK}=\frac{GH}{KL}$. We know $FG = 45$, $JK = 15$, and $GH=40.2$. So the proportion is $\frac{45}{15}=\frac{40.2}{KL}$.

Step2: Cross - multiply

Cross - multiplying gives us $45\times KL=15\times40.2$.

Step3: Solve for KL

First, calculate $15\times40.2 = 603$. Then $KL=\frac{603}{45}=13.4$.

Answer:

$13.4$