SOLUTION: A ladder is leaning against a building. The distance from he bottom of the ladder to the building is 18 ft shorter than the length out the ladder. How high up the side of the build
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Question 1068857: A ladder is leaning against a building. The distance from he bottom of the ladder to the building is 18 ft shorter than the length out the ladder. How high up the side of the building is the top of the ladder of the distance is 9 ft less than the length of the ladder? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A ladder is leaning against a building.
The distance from the bottom of the ladder to the building is 18 ft shorter than the length out the ladder.
How high up the side of the building is the top of the ladder if the distance is 9 ft less than the length of the ladder?
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The ladder forms a right triangle, the length of the ladder is the hypotenuse
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let L = the length of the ladder
then
(L-18) = distance from the bottom of the ladder to the building
and
(L-9) = how high up the building is the top of the ladder.
Pythag
(L-18)^2 + (L-9)^2 = L^2
FOIL
(L^2 - 36L + 324) + (L^2 - 18L + 81) = L^2
Combine like terms on the right
L^2 + L^2 - L^2 - 36L - 18L + 324 + 81 = 0
L^2 - 54L + 405 = 0
You can use the quadratic formula, but this will factor to
(L-45)(L-9) = 0
L = 9
and
L = 45 ft is the reasonable answer for the length of the ladder
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Check on a calc: enter
