SOLUTION: A ladder is resting against a wall. The top of teh ladder touches the wall at a height of 12 feet. Find the distance from the wall to the bottom of teh ladder if the length of teh

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Question 175284: A ladder is resting against a wall. The top of teh ladder touches the wall at a height of 12 feet. Find the distance from the wall to the bottom of teh ladder if the length of teh ladder is 12 feet less than twice its distance from the wall.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the distance from the bottom of the ladder to the base of the wall be x.
The length of the ladder is 2x-12.
The right triangle formed by the wall at the point where the ladder touches it (12) is the triangle's height.
The base of the triangle is x and the hypotenuse is the ladder of length (2x-12).
Using the Pythagorean theorem:c%5E2+=+a%5E2%2Bb%5E2 where c = 2x-12, a = 12 and b = x.
%282x-12%29%5E2+=+12%5E2%2Bx%5E2 Simplify.
4x%5E2-48x%2B144+=144%2Bx%5E2 Subtract x^2 from both sides.
3x%5E2-48x%2B144+=+144 Subtract 144 from both sides.
3x%5E2-48x+=+0 Add 48x to both sides.
3x%5E2+=+48x Divide both sides by 3x.
x+=+16
The distance from the bottom of the ladder to the base of the wall is 16 feet.