Question

use the image to answer the question

△jkl∼△pkq, and (overline{kp}=14m), (overline{jk}=56m), and (overline{kq}=21m). what is the length of (overline{kl})?
(1 point)
5.25 m
84 m
34 m
72 m

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle JKL\sim\triangle PKQ\), the ratios of corresponding sides are equal. That is \(\frac{JK}{PK}=\frac{KL}{KQ}\).
We know that \(JK = 56\space m\), \(PK=\overline{KP}=14\space m\), and \(KQ = 21\space m\). Substitute these values into the proportion \(\frac{56}{14}=\frac{KL}{21}\).

Step2: Solve the proportion for \(KL\)

First, simplify \(\frac{56}{14}=4\). So the equation becomes \(4=\frac{KL}{21}\).
Multiply both sides of the equation by \(21\): \(KL=4\times21\).

Answer:

\(84\space m\)