Question

triangle nop is similar to triangle qrs. find the measure of side qr. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
triangle nop: p to o is 11, o to n is 21.
triangle qrs: r to s is 38.

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle NOP \sim \triangle QRS\), corresponding sides are proportional. Side \(PO = 11\) in \(\triangle NOP\) corresponds to side \(RS = 38\) in \(\triangle QRS\), and side \(NO = 21\) in \(\triangle NOP\) corresponds to side \(QR\) in \(\triangle QRS\).

Step2: Set Up Proportion

Let \(QR = x\). The proportion is \(\frac{PO}{RS}=\frac{NO}{QR}\), so \(\frac{11}{38}=\frac{21}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(11x = 38\times21\). Calculate \(38\times21 = 798\). Then \(x=\frac{798}{11}\approx72.5\) (rounded to the nearest tenth).

Answer:

\(72.5\)