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

84 m
84 m

72 m
72 m

5.25 m
5.25 m
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Answer 1

Because △JKL ∼ △PKQ with J↔P, K↔K, L↔Q, the scale factor is PK/JK = 14/56 = 1/4. Thus KQ/KL = 1/4, so KL = 4·KQ = 4·21 = 84 m.

Answer: 84 m