SOLUTION: A ladder of length 2x+2 feet is positioned against a wall such that the bottom is x-2 feet away from the wall. The distance between the floor and the top of the ladder is 2x feet.

Question 918892: A ladder of length 2x+2 feet is positioned against a wall such that the bottom is x-2 feet away from the wall. The distance between the floor and the top of the ladder is 2x feet.
Find the length in feet
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A ladder of length 2x+2 feet is positioned against a wall such that the bottom is x-2 feet away from the wall. The distance between the floor and the top of the ladder is 2x feet.
Find the length in feet
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Draw the picture.
You have a right triangle with:
hypotenuse = 2x+2
base = x-2
height = 2x
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Use Pythagoras to solve for "x"::
(2x+2)^2 = (x-2)^2 + (2x)^2
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4x^2 + 8x + 4 = x^2 - 4x + 4 + 4x^2
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x^2 -12x = 0
x(x-12) = 0
Positive solution::
x = 12 ft
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Ans: Length of the ladder = 2x+2 = 26 ft.
Cheers,
Stan H.
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