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 corresponding sides are proportional. The side \(PN = 5\) in \(\triangle NOP\) corresponds to side \(QS = 21\) in \(\triangle QRS\), and side \(OP = 9\) in \(\triangle NOP\) corresponds to side \(RS\) in \(\triangle QRS\).

Step2: Set up proportion

Let \(RS = x\). The proportion of corresponding sides is \(\frac{PN}{QS}=\frac{OP}{RS}\), so \(\frac{5}{21}=\frac{9}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(5x = 21\times9\). Calculate \(21\times9 = 189\), so \(5x=189\). Then \(x=\frac{189}{5}=37.8\).

Answer:

\(37.8\)