Question 337650
A ladder is leaning against a house and the base of the ladder is 15 feet from the house. When the bottom of the ladder is pulled 9 feet farther away from the house, the upper end of the ladder slides 13 feet down. How long (in feet) is the ladder?
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Draw a diagram of the problem.  It'll help you see the solution.
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Apply Pythagorean theorem:
Let x = length of ladder
and
Let y = upper end of ladder when it is 15 ft from house
then we have two equations:
x^2 = 15^2 +y^2
x^2 = 24^2 + (y-13)^2
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Solve for y:
15^2 +y^2 = 24^2 + (y-13)^2
225 +y^2 = 576 + (y-13)(y-13)
225 +y^2 = 576 + y^2-26y+169
225 +y^2 = y^2-26y+745
225 = -26y+745
-520 = -26y
20 ft = y
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Plug the above into equation 1 and solve for x:
x^2 = 15^2 +y^2
x^2 = 15^2 +20^2
x^2 = 225 + 400
x^2 = 625
x = 25 feet (length of ladder)