SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. How high up the building is the top

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 8 ft less than the length of the ladder. How high up the building is the top       Log On


   

Question 1014773: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder.
Answer by stanbon(75887) About Me  (Show Source):
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A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder.
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Sketch the picture.
You have a right triangle
base = x-8
hypotenuse ladder = x
height = x-1
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Equation::
x^2 = (x-8)^2 + (x-1)^2
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x^2 = x^2 - 16x + 64 + x^2 - 2x + 1
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x^2 = 2x^2 - 18x +65
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x^2 -18x+65 = 0
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x = 13 or x = 5
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Acceptable answer: x = 13
Ans: height = x-1 = 12
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Cheers,
Stan H.