Question

triangle lmn is similar to triangle opq. find the measure of side op. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
n 17 m
27
l
p 59 q
o
answer attempt 1 out of 2

Explanation:

Step1: Identify corresponding sides

Since \(\triangle LMN \sim \triangle OPQ\), the corresponding sides are proportional. In \(\triangle LMN\), \(NM = 17\) and \(LM = 27\). In \(\triangle OPQ\), \(QP = 59\) and \(OP\) corresponds to \(LM\), \(QP\) corresponds to \(NM\). So the proportion is \(\frac{LM}{OP}=\frac{NM}{QP}\).

Step2: Set up the proportion

Substitute the known values: \(\frac{27}{OP}=\frac{17}{59}\).

Step3: Solve for \(OP\)

Cross - multiply: \(17\times OP = 27\times59\). Then \(OP=\frac{27\times59}{17}\). Calculate \(27\times59 = 1593\), so \(OP=\frac{1593}{17}\approx93.7\) (rounded to the nearest tenth).

Answer:

\(93.7\)