SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16ft shorter than the length of the ladder. How high up the side of the buildi

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Question 370605: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 8ft less than the length of the ladder?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the information given, the hypotenuse is l, the horizontal leg is l - 16, and the vertical leg is l - 8. Using the Pythagorean theorem, then l%5E2+=+%28l-8%29%5E2%2B%28l-16%29%5E2.
l%5E2+=+l%5E2-16l%2B64+%2B+l%5E2+-+32l%2B256, or
0+=+l%5E2+-+48l%2B320, or
0 = (l-40)(l-8). Thus l = 40 ft or l = 8 ft. We discard the 2nd value (why?) Thus the length of the ladder is 40 feet.