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 ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable 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 326200: 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The ladder, ground, and wall form a right triangle.
Use the Pythagorean theorem to solve.
A%5E2%2BB%5E2=H%5E2
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A=H-4
B=H-2
A%5E2%2BB%5E2=H%5E2
%28H-4%29%5E2%2B%28H-2%29%5E2=H%5E2
H%5E2-8H%2B16%2BH%5E2-4H%2B4=H%5E2
2H%5E2-12H%2B20=H%5E2
H%5E2-12H%2B20=0
+%28H-10%29%28H-2%29=0+
Two solutions:
H-2=0
H=2
Not allowed since A=H-4=-2, can't have a negative length.
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H-10=0
H=10
A=10-4=6
B=10-2=8
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The ladder is 10 ft long, the base of the ladder is 8 ft from the wall, and the top of the ladder is 6 ft from the ground.