Question

triangle nop is similar to triangle rst. find st. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle NOP\sim\triangle RST\), the ratios of corresponding sides are equal. Let \(ST = x\). We have the proportion \(\frac{OP}{ST}=\frac{NO}{RS}\). Substituting the values \(OP = 10\), \(NO=17\), and \(RS = 60\), we get \(\frac{10}{x}=\frac{17}{60}\).

Step2: Cross - multiply

Cross - multiplying gives us \(17x=10\times60\). So, \(17x = 600\).

Step3: Solve for \(x\)

Dividing both sides by \(17\), \(x=\frac{600}{17}\approx35.3\).

Answer:

\(35.3\)