Question

triangle opq is similar to triangle rst. find the measure of side rs. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle OPQ\sim\triangle RST\), the ratios of corresponding sides are equal. That is \(\frac{OP}{RS}=\frac{OQ}{RT}\).

Step2: Substitute the known values

We know \(OP = 17\), \(OQ = 36\), and \(RT = 7\). Substituting into the proportion \(\frac{17}{RS}=\frac{36}{7}\).

Step3: Solve for \(RS\)

Cross - multiply gives \(36\times RS=17\times7\). So \(36RS = 119\). Then \(RS=\frac{119}{36}\approx3.3\).

Answer:

\( RS = 3.3 \)