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.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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.       Log On


   

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) About Me  (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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