Question

proving similar triangles quick check
(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)
84 m
34 m
72 m
5.25 m

Explanation:

Step1: Find the ratio of corresponding sides

Since \(\triangle JKL\sim\triangle PKQ\), the ratio of corresponding sides is \(\frac{JK}{PK}\). Given \(JK = 56\) m and \(KP=14\) m, then \(\frac{JK}{PK}=\frac{56}{14} = 4\).

Step2: Use the ratio to find \(KL\)

We know that \(\frac{KL}{KQ}=4\) (because of the similarity of triangles \(\triangle JKL\) and \(\triangle PKQ\)). Given \(KQ = 21\) m. Let \(KL=x\), then \(x=4\times KQ\).
Substitute \(KQ = 21\) m into the equation: \(x = 4\times21\).

Answer:

\(84\) m