Question

similar figures / proportion (level 1)
question
triangle lmn is similar to triangle opq. find the measure of side pq. round your answer to the nearest tenth if necessary.

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 \(\frac{LM}{OP}=\frac{MN}{PQ}\). Substituting the known values: \(\frac{9}{40}=\frac{4}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(9x = 4\times40\). So, \(9x=160\).

Step3: Solve for \(x\)

Dividing both sides by 9: \(x=\frac{160}{9}\approx17.8\).

Answer:

\(17.8\)