SOLUTION: A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How

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Question 272948: A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?
Answer by dabanfield(803) About Me  (Show Source):
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A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?
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If we let x be the distance from the top of the ladder to the foot of the wall the we have a right triangle with hypotenuse 13 and sides x aqnd x-7. By the Pythagorean Theorem we have then:
x^2 + (x-7)^2 = 13^2
x^2 + x^2 - 14x + 49 = 169
2x^2 - 14x - 120 = 0
Divide both sides by 2:
x^2 - 7x - 60 = 0
(x-12)*(x+5) = 0
x-12 = 0
x = 12
or
x+5 = 0
x = -5
Since x must be positive we x=12. So x-7 = 5