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

Algebra ->  Triangles -> SOLUTION: A 13-ft ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 ft less than the distance from the top of the ladder to the ground. How fa      Log On


   

Question 3780: A 13-ft ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 ft 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 longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
ladder against a house...forms a right-angled triangle. So this means Pythagoras' Theorem.

Let the height of the ladder against the wall = x
so the base of the ladder is x-7.

Pythagoras states (for this triangle) 13%5E2+=+x%5E2+%2B+%28x-7%29%5E2
169+=+x%5E2+%2B+x%5E2+-+14x+%2B+49
0+=+2x%5E2+-+14x+-+120
or
x%5E2+-+7x+-+60+=+0

(x+5)(x-12) = 0

so, either x+5=0 or x-12 = 0

so x=-5 or x=12.

Therefore height of ladder = 12feet and base of ladder is 12-7 = 5feet away.

jon