SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista

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Question 150818: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.
Answer by nerdybill(7384) (Show Source):
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A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.
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Apply Pythagorean theorem:
The wall, the ground and the ladder forms a right triangle.
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Let x = length of the ladder
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(x-3)^2 + (x-4)^2 = x^2
(x^2-6x+9) + (x^2-8x+16) = x^2
2x^2 - 14x + 25 = x^2
x^2 - 14x + 25 = 0
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Can't factor so you must use the quadratic equation. In doing so, it will yield two solutions:
x = {11.899, 2.101}
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Obviously, a 2 foot ladder does not make sense therefore:
length of ladder = 11.899 feet
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Below is the quadratic solution:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=96 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 11.8989794855664, 2.10102051443364. Here's your graph: