Question

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

Explanation:

Step1: Identify corresponding sides

Since $\triangle NOP \sim \triangle QRS$, the ratio of corresponding sides is equal. Let's assume $PN$ corresponds to $QS$ and $PO$ corresponds to $RS$. So, $\frac{PN}{QS}=\frac{PO}{RS}$.
Given $PN = 55$, $QS = 21$, $PO = 41$. Let $RS = x$.

Step2: Set up proportion

We have $\frac{55}{21}=\frac{41}{x}$.

Step3: Solve for x

Cross - multiply: $55x=21\times41$.
Calculate $21\times41 = 861$.
Then $x=\frac{861}{55}\approx15.6545\approx15.7$ (rounded to the nearest tenth).

Answer:

The measure of side $RS$ is approximately $15.7$.