SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 4 ft less than the length of the ladder. How high up the side of the building

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 4 ft less than the length of the ladder. How high up the side of the building       Log On


   

Question 1014409: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 4 ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 2 ft less than the length of the​ ladder?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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C=L=length of ladder; A=height up side of building=L-2;
B=distance from building to bottom of ladder=L-4
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A%5E2%2BB%5E2=C%5E2
%28L-2%29%5E2%2B%28L-4%29%5E2=L%5E2
%28L%5E2-4L%2B4%29%2B%28L%5E2-8L%2B16%29=L%5E2
2L%5E2-12L%2B20=L%5E2
L%5E2-12L%2B20=0
%28L-2%29%28L-10%29=0
L-2=0 OR L-10=0
L=2 OR L=10
Since L must be greater than 4 (Distance from building is L-4),
L=10.
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ANSWER: Length of ladder is 10 feet.
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CHECK:
C=L=10 feet
A=L-2=10-2=8 feet
B=L-4=10-4=6 feet
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A%5E2%2BB%5E2=C%5E2
8%5E2%2B6%5E2=10%5E2
64%2B36=100
100=100