SOLUTION: The front of an A-frame cabin in a national park is in the shade of a triangle, with an area of 189 ft^2. If the height is 1 ft less than twice the base, find the base and the heig

Question 1036057: The front of an A-frame cabin in a national park is in the shade of a triangle, with an area of 189 ft^2. If the height is 1 ft less than twice the base, find the base and the height of the front of the cabin?

Found 2 solutions by stanbon, fractalier:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The front of an A-frame cabin in a national park is in the shape of a triangle, with an area of 189 ft^2. If the height is 1 ft less than twice the base, find the base and the height of the front of the cabin?
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A = (1/2)*base*height
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189 = (1/2)*b*(2b-1)
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378 = 2b^2 - 2b
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2b^2 - 2b - 378 = 0
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b^2 - b - 189 = 0
Use the Quadratic formula to get::
base = 14.26 ft
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height = 2b-1 = 28.52-1 = 27.52 ft
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Cheers,
Stan H.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
The area of a triangle is of course

Here A = 189 and h = 2b - 1...plugging in gives us
189 = (1/2)(b)(2b-1)
378 = 2b^2 - b
2b^2 - b - 378 = 0
and if you solve this you get
(2b + 27)(b - 14)=0 and
b = 14 or b = -13.5
The base has to be 14 ft and the height is 2(14)-1 = 27 ft.
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