Question

triangle lmn is similar to triangle opq. find the measure of side pq. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle LMN\sim\triangle OPQ\), the ratios of corresponding sides are equal. Let \(PQ = x\). The proportion is \(\frac{LM}{OP}=\frac{LN}{OQ}\). Substituting the values, we have \(\frac{72}{x}=\frac{36}{9.2}\).

Step2: Cross - multiply

Cross - multiplying gives \(36x=72\times9.2\).

Step3: Solve for \(x\)

First, calculate \(72\times9.2 = 662.4\). Then, \(x=\frac{662.4}{36}\).

$$x = 18.4$$

Answer:

\(18.4\)