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.
triangle lmn has sides: ln = 11, lm = 5. triangle opq has side op = 21.

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle LMN \sim \triangle OPQ\), corresponding sides are proportional. Let's assume \(LM\) corresponds to \(OP\), and \(LN\) corresponds to \(OQ\). So \(LM = 5\), \(OP = 21\), \(LN = 11\), and we need to find \(OQ\) (which is \(QO\)).

Step2: Set Up Proportion

The proportion for similar triangles is \(\frac{LM}{OP}=\frac{LN}{OQ}\). Substituting the known values: \(\frac{5}{21}=\frac{11}{QO}\).

Step3: Solve for \(QO\)

Cross - multiply: \(5\times QO=21\times11\). Then \(5QO = 231\). Divide both sides by 5: \(QO=\frac{231}{5}=46.2\).

Answer:

The measure of side \(QO\) is \(46.2\).