SOLUTION: how do you find the area of a right triangle if you only know the length of the hypotenuse (6)and the perimeter (14)

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Question 411412: how do you find the area of a right triangle if you only know the length of the hypotenuse (6)and the perimeter (14)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do you find the area of a right triangle if you only know the length of the hypotenuse (6)and the perimeter (14)
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Area = base*height
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Perimeter = base + height + hypotenuse = 14
b + h +6 = 14
b + h = 8
b = 8-h
b^2 = (8-h)^2
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Using Pythagoras:
b^2 + h^2 = 6^2
b^2 = 36-h^2
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Solve for "b":
(8-h)^2 = 36- h^2
64-16h+h^2 = 36-h^2
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2h^2-16h+28 = 0
h^2-8h+14 = 0
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h = [8 +- sqrt(64-4*14)]/2
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h = [8 +- sqrt(8)]/2
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Positive solution:
h = 4+sqrt(2)
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Solve for "b":
b^2 = 36-h^2
h^2 = (4+sqrt(2))^2 = 16+8sqrt(2)+2 = 18+8sqrt(2)
b^2 = 36-(18+8sqrt(2)
b^2 = 18-8sqrt(2)
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Area = (1/2)bh
Area = (1/2)(sqrt[18-8sqrt(2)])[4+sqrt(2)]
etc.
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Cheers,
Stan H.
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