Question

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

Explanation:

Step1: Identify corresponding sides

Since \(\triangle LMN \sim \triangle OPQ\), the corresponding sides are proportional. Let's assume \(LN\) corresponds to \(QO\) and \(MN\) corresponds to \(PQ\). So, \(LN = 25\), \(MN = 14\), and \(PQ = 47\).

Step2: Set up proportion

The proportion is \(\frac{LN}{QO}=\frac{MN}{PQ}\). Substituting the known values, we get \(\frac{25}{QO}=\frac{14}{47}\).

Step3: Solve for \(QO\)

Cross - multiply: \(14\times QO = 25\times47\). Then \(QO=\frac{25\times47}{14}\). Calculate \(25\times47 = 1175\), so \(QO=\frac{1175}{14}\approx83.9\).

Answer:

\(83.9\)