Question

1. triangle ghi is similar to triangle jkl. find the measure of side kl. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let $KL = x$. We have the proportion $\frac{KL}{HI}=\frac{JL}{GI}$. Here, $HI = 41$, $JL = 5$, and $GI=23$. So the proportion is $\frac{x}{41}=\frac{5}{23}$.

Step2: Solve for $x$

Cross - multiply: $23x = 41\times5$. Then $23x=205$. Divide both sides by 23: $x=\frac{205}{23}\approx8.9$.

Answer:

$8.9$