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A right triangle has hypotenuse 10. If its perimeter is 25,

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by Max@Math Revolution » Tue Apr 02, 2019 6:56 am
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[GMAT math practice question]

A right triangle has hypotenuse 10. If its perimeter is 25, what is its area?

A. 125/4
B. 125/2
C. 125
D. 225/4
E. 225/2
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by Max@Math Revolution » Wed Apr 03, 2019 11:29 pm
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Let a and b be the legs of the right triangle.
Since the hypotenuse is 10, a^2+b^2=100.
Since the triangle’s perimeter is 25, we have a + b + 10 = 25 and a + b = 15.
Recall that (a+b)^2 = a^2 + 2ab + b^2.
2ab = (a+b)^2 – (a^2+b^2) = 225 – 100 = 125.
Thus, the area of the triangle is (1/2)ab = 125 / 4.

Therefore, A is the answer.
Answer: A
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