SOLUTION: If the area of a right triangle is 24 square inches and the hypotenuse is 12 inches, find the lengths of the legs of the triagle.

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Question 350112: If the area of a right triangle is 24 square inches and the hypotenuse is 12 inches, find the lengths of the legs of the triagle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be the legs of the triangle.
A=%281%2F2%29xy=24
1.xy=48
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.
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2.x%5E2%2By%5E2=12%5E2
Find the intersection points between these two functions.
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.
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From eq. 1,
y=48%2Fx
y%5E2=2304%2Fx%5E2
Substitute into eq. 2,
x%5E2%2B2304%2Fx%5E2=144
x%5E4-144x%5E2%2B2304=0
x%5E4-144x%5E2%2B5184%2B2304=5184
%28x%5E2-72%29%5E2%2B2304=5184
%28x%5E2-72%29%5E2=2880
%28x%5E2-72%29%5E2=64%2A9%2A5
x%5E2-72=0+%2B-+8%2A3%2Asqrt%285%29
x%5E2=72+%2B-+24sqrt%285%29
or approximately,
x1=11.21 and x2=4.28
with corresponding y values of
y1=4.28 and y2=11.21