Question

triangle hij is similar to triangle klm. find the measure of side kl. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since $\triangle HIJ \sim \triangle KLM$, the corresponding sides are proportional. So, $\frac{HI}{KL}=\frac{JI}{ML}$.
We know $HI = 7.5$, $JI = 9$, and $ML = 41$. Let $KL = x$.

Step2: Set up proportion and solve

Set up the proportion: $\frac{7.5}{x}=\frac{9}{41}$.
Cross - multiply: $9x=7.5\times41$.
Calculate $7.5\times41 = 307.5$.
Then $x=\frac{307.5}{9}$.
Simplify: $x = 34.166\cdots\approx34.2$ (rounded to the nearest tenth).

Answer:

34.2