SOLUTION: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12ft. Find the length of the ladder if the length is 4ft more than its distance from the w
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Question 1135394: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12ft. Find the length of the ladder if the length is 4ft more than its distance from the wall. Found 2 solutions by rothauserc, jim_thompson5910:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! let the distance of the ladder from the wall be x
:
Use Pythagorean Theorem
:
12^2 +x^2 = (x+4)^2
:
144 +x^2 = x^2 +8x +16
:
8x = 128
:
x = 16
:
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the length of the ladder is 16 +4 = 20 feet
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:
You can put this solution on YOUR website!
x = distance from the bottom of the wall to the base of the ladder
x+4 = length of ladder (since it's 4 more feet compared to the previous distance)
12 = height where the ladder touches at the top of the wall
Diagram:
We have a right triangle with legs of x and 12. The hypotenuse is x+4
Use the Pythagorean theorem to get...
a = x, b = 12, c = x+4
a^2 + b^2 = c^2
x^2 + 12^2 = (x+4)^2
x^2 + 144 = x^2+8x+16
144 = 8x+16 .... subtract x^2 from both sides
144-16 = 8x .... subtract 16 from both sides
128 = 8x
8x = 128
x = 128/8
x = 16
The distance from the base of the ladder to the bottom of the wall is 16 feet.
Use this x value to compute the expression x+4
x+4 = 16+4 = 20
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