SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 9ft less than the length of the ladder. How high up the side of the building

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 9ft less than the length of the ladder. How high up the side of the building       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 204638: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 9ft less than the length of the ladder. How high up the side of the building is the top of the ladder if the distance is 2ft less than the length of the ladder?
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
the illustration for the problem should be a right triangle with:
hypotenuse = the length of the ladder = L
horizontal side = distance from bottom of the ladder to the building = L - 9
vertical side = distance from top of the ladder to the bottom of the building = L - 2

so,we can use Phytagoras formula:
%28L+-+9%29%5E2+%2B+%28L+-+2%29%5E2+=+L%5E2
L%5E2+-+18L+%2B+81+%2B+L%5E2+-+4L+%2B+4+=+L%5E2
L%5E2+-+18L+%2B+81+%2B+L%5E2+-+4L+%2B+4+-+L%5E2+=+0
L%5E2+-+22L+%2B+85+=+0
(L - 5)(L - 17) = 0
L = 5 or L = 17

L = 17, because if L = 5 is used, the horizontal side will be in negative value

so, if L = 17, then the top of the ladder will reach the building (17 - 2) = 15 ft from the bottom