SOLUTION: A ladder leans against a barn with its base 15 feet from the barn. when the ladder is pulled 9 feet further away from the barn, the upper end slides down 13 feet. how long is the l

Question 358130: A ladder leans against a barn with its base 15 feet from the barn. when the ladder is pulled 9 feet further away from the barn, the upper end slides down 13 feet. how long is the ladder?
So far I have tried the Pythagorean theorem but I am not sure where to plug which numbers into. I also know that the ladder is a total of 24 feet away from the barn. Please help me, thanks so much.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A ladder leans against a barn with its base 15 feet from the barn. when the ladder is pulled 9 feet further away from the barn, the upper end slides down 13 feet. how long is the ladder?
.
The "ladder" is always the hypotenuse.
.
Before the slide:
Let x = height where the ladder hits the barn
and y = ladder's length
then
x^2 + 15^2 = y^2 (equation 1)
.
After the slide:
(x-9)^2 + (15+9)^2 = y^2
(x-9)^2 + (24)^2 = y^2 (equation 2)
.
Since equation 1 and equation 2 both defines y^2 we have:
x^2 + 15^2 = (x-9)^2 + (24)^2
x^2 + 225 = (x-9)^2 + 576
x^2 + 225 = (x-9)(x-9) + 576
x^2 + 225 = (x^2-18x+81) + 576
x^2 + 225 = x^2-18x+657
225 = -18x+657
-432 = -18x
24 = x
.
To find y (the ladder's length) plug the above back into equation 1 and solve for y:
x^2 + 15^2 = y^2
24^2 + 15^2 = y^2
576 + 225 = y^2
801 = y^2
28.3 feet = y (ladder's length)

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