SOLUTION: A 13-foot ladder is resting at an angle against a building. The distance from the bottom of the ladder to the edge of the building is 7 feet less than the distance from the top of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A 13-foot ladder is resting at an angle against a building. The distance from the bottom of the ladder to the edge of the building is 7 feet less than the distance from the top of      Log On


   

Question 852: A 13-foot ladder is resting at an angle against a building. The distance from the bottom of the ladder to the edge of the building is 7 feet less than the distance from the top of the ladder down to the ground. What is the height at which the ladder touches the building and what is the distance from the bottom of the ladder to the building??
Answer by usyim88hk(158) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the distance from the bottom of the ledder to the edge of the building:
We can then come up with an equation
x^2+(x+7)^2 = 13^2
Now solve for (x+7)^2
(x+7)(x+7)
=x(x+7)+7(x+7)
=x^2+7x+7x+49
=x^2+14x+49
Now we put this back to the previous equation x^2+(x+7)^2 = 13^2
x^2+x^2+14x+49=169
2x^2+14x+49-169=169-169
2x^2+14x-120=0
Now use the qurdratic formula
+x=%28%28-14%2B-sqrt%28%2814%5E2%29-4%282%29%28-120%29%29%29%2F%282%282%29%29%29
+x=%28%28-14%2B-sqrt%28196%2B960%29%29%2F4%29+
+x=%28%28-14%2B-34%29%2F4%29
x = -48/4 or 20/4
x = -12 or 5
Since length cannot be a negative number, -12 is not the answer, so 5 is the answer.
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Check:
5^2+(5+7)^2 = 13^2
25+144 = 169
169=169 (Correct!!!)