SOLUTION: A 26ft. long ladder rest against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rest against the wall is x + 14. Fi

Question 339347: A 26ft. long ladder rest against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rest against the wall is x + 14. Find the distance, x, from the base of the wall to the bottom of the ladder.
I have drawn out a figure and listed the information given and then I am stuck. I just can't seem to put this one together, maybe my brain is just too tired?
Thank you in advance for your help!!
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A 26ft. long ladder rest against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rest against the wall is x + 14. Find the distance, x, from the base of the wall to the bottom of the ladder.
.
Apply the Pythagorean theorem:
.
x^2 + (x+14)^2 = 26^2
x^2 + (x+14)(x+14) = 676
x^2 + (x^2+14x+14x+196) = 676
2x^2 + 28x + 196 = 676
dividing both sides by 2:
x^2 + 14x + 98 = 338
x^2 + 14x - 240 = 0
(x+24)(x-10) = 0
x = {-24, 10}
We can toss out the negative solution leaving:
x = 10 feet

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