Question

quadrilateral lmno is similar to quadrilateral pqrs. find the measure of side pq. round your answer to the nearest tenth if necessary.

(diagrams of quadrilaterals lmno and pqrs are shown, with lm = 13, nm = 17 in lmno; rq = 55 in pqrs)

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals LMNO and PQRS are similar, the ratio of corresponding sides is equal. Side MN (length 17) in LMNO corresponds to side QR (length 55) in PQRS, and side LM (length 13) in LMNO corresponds to side PQ (length \( x \)) in PQRS.

Step2: Set up proportion

The proportion is \(\frac{LM}{PQ} = \frac{MN}{QR}\), which becomes \(\frac{13}{x} = \frac{17}{55}\).

Step3: Solve for \( x \)

Cross - multiply: \(17x = 13\times55\).
Calculate \(13\times55 = 715\).
Then \(x=\frac{715}{17}\approx42.1\).

Answer:

The measure of side PQ is approximately \(42.1\).