SOLUTION: A 20m ladder and a 15m ladder were leaned against a building. The botom of the longer ladder was 7m farther from the bottom of the building than the shorter ladder, but both ladder

Question 636469: A 20m ladder and a 15m ladder were leaned against a building. The botom of the longer ladder was 7m farther from the bottom of the building than the shorter ladder, but both ladders reached the same distance up the building. Find the distance.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
We have two right triangles with same height, h, for one of the legs and the other legs are d and 7 + d, and the two hypotenuses are 15 and 20 respectively. Using the Pythagorean Theorem we have:
(1) 20^2 = h^2 + (d+7)^2 and
(2) 15^2 = h^2 + d^2
Expanding (1) we have
400 = h^2 + d^2 + 2*7*d + 7^2
(3) 400 = h^2 + d^2 + 14*d + 49
Substitute (2) into (3) yields
400 = 15^2 + 14*d + 49
(4) 400 = 225 + 14*d + 49
or 14*d = 400 - 225 - 49
14*d = 126
(5) d = 9
Answer: The shorter ladder is 9m from the building and the longer ladder is 16m from the building. By the way they each reach 12m up the building.

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