SOLUTION: a ladder is leaning against a building.the distance from the bottom of the ladder to the building is 9ft less than the length of the ladder.How high up the side of the building is

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Question 362908: a ladder is leaning against a building.the distance from the bottom of the ladder to the building is 9ft less than the length of the ladder.How high up the side of the building is the top of the ladder is the distance is 2ft less than the length of the ladder?
the ladder reaches __ feet up the wall
Answer by mananth(16946) About Me  (Show Source):
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a ladder is leaning against a building.the distance from the bottom of the ladder to the building is 9ft less than the length of the ladder.How high up the side of the building is the top of the ladder is the distance is 2ft less than the length of the ladder?
the ladder reaches __ feet up the wall
...
ladder = x
ground distance of ladder = x-9
height ladder rests = x-2
..
they form a right triangle with ladder as the hypotenuse
x^2=(x-9)^2+(x-2)^
x^2=x^2-18x+81+x^2-4x+4
2x^2-x^2-22x+85=0
x^2-22x+85=0
x^2-17x-5x+85=0
x(x-17)-5(x-17)=0
(x-17)(x-5)=0
x= 17 feet height the ladder touches the wall
m.ananth@hotmail.ca