SOLUTION: New chapter/Homework problem. Set up and Solve equation using the zero-factor property. Word problem. thanks! A ladder forms a right triangle with the ground and one wall of

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Question 76287: New chapter/Homework problem. Set up and Solve equation using the zero-factor property. Word problem. thanks!
A ladder forms a right triangle with the ground and one wall of a building. the base of the triangle is 5 feet less than the height. If the area of the triangle is 18 square feet, find the height?
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula for the area of a triangle:
A=1/2(base)(height)
Area=18
Base=height - 5 feet
Height=h
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Plug-in the values and solve.
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A=1/2(base)(height)
18=(1/2)(h-5)(h)
18=(1/2)(h^2-5h)
(2)(18)=(2)(1/2)(h^2-5h)
36=h^2-5h
36-36=h^2-5h-36
0=h^2-5h-36
0=(h-9)(h+4)
h=9
or h=-4 (eliminate this answer since a measurement cannto be a negative number]
.
Check by plugging all of the values back into the original equation:
A=1/2(base)(height)
18=(1/2)(9-5)(9)
18=(1/2)(4)(9)
18=18 [checks out]