SOLUTION: Please help me solve this problem: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is

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Question 886807: Please help me solve this problem: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is 2 feet more than it's distance from the wall.
Answer by nerdybill(7384) (Show Source):
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Please help me solve this problem: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is 2 feet more than it's distance from the wall.
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Let x = distance from wall
then from "ladder if the length is 2 feet more than it's distance from the wall"
we have
x+2 = length of ladder
.
applying Pythagorean theorem:
x^2 + 6^2 = (x+2)^2
x^2 + 36 = (x+2)(x+2)
x^2 + 36 = x^2+4x+4
36 = 4x+4
32 = 4x
8 feet = x (distance from wall)
,
length of ladder:
x+2 = 8+2 = 10 feet