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

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) (Show Source): You can put this solution on YOUR website!
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?
0 solutions
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

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