Question

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

Explanation:

Step1: Identify corresponding sides

Since $\triangle KLM \sim \triangle NOP$, the corresponding sides are proportional. So, $\frac{KM}{PN}=\frac{KL}{ON}$.
We know $KM = 41$, $KL = 23$, and $ON = 7$.

Step2: Set up the proportion and solve for $PN$

From the proportion $\frac{41}{PN}=\frac{23}{7}$, we can cross - multiply to get $23\times PN=41\times7$.
First, calculate $41\times7 = 287$. Then, $PN=\frac{287}{23}$.

Step3: Calculate the value of $PN$

$\frac{287}{23}\approx12.5$ (rounded to the nearest tenth).

Answer:

The measure of side $PN$ is approximately $12.5$.