Question

Use the image to answer the question.

Triangle upper J upper K upper L is divided into triangle upper P upper K upper Q and quadrilateral upper J upper P upper Q upper L by vertical line upper P upper Q. Point upper P is on line upper J upper K. Point upper Q is on diagonal upper L upper K.

△JKL∼△PKQ
, and KP¯¯¯¯¯¯¯¯=14
m, JK¯¯¯¯¯¯¯¯=56
m, and KQ¯¯¯¯¯¯¯¯=21
m. What is the length of KL¯¯¯¯¯¯¯¯
?

(1 point)
Responses

34 m
34 m

72 m
72 m

84 m
84 m

5.25 m

Answer 1

Since △JKL ∼ △PKQ with corresponding vertices J→P, K→K, L→Q, the scale factor is KP/JK = 14/56 = 1/4. Thus KQ = (1/4)KL, so KL = 4·KQ = 4·21 = 84 m.