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
84 m
84 m
34 m
34 m
72 m
72 m
5.25 m
To find the length of KL, we can set up a proportion based on the similarity of the triangles:
KP/JK = KQ/KL
Substituting the given values, we have:
14/56 = 21/KL
Cross-multiplying, we have:
14 * KL = 56 * 21
Dividing both sides by 14, we get:
KL = (56 * 21) / 14
Simplifying, we have:
KL = 4 * 21
KL = 84
Therefore, the length of KL is 84 meters.