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Isosceles right triangle ABC has an area of 72. What is its perimeter?

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by AAPL » Wed Aug 26, 2020 9:27 am
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Isosceles right triangle ABC has an area of \(72\). What is its perimeter?

A. \(12+6\sqrt{2}\)
B. \(16+8\sqrt{2}\)
C. \(18+9\sqrt{2}\)
D. \(20+10\sqrt{2}\)
E. \(24+12\sqrt{2}\)

OA E
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Re: Isosceles right triangle ABC has an area of 72. What is its perimeter?

by Scott@TargetTestPrep » Sun Aug 30, 2020 7:27 am
AAPL wrote: ↑
Wed Aug 26, 2020 9:27 am
 Veritas Prep

Isosceles right triangle ABC has an area of \(72\). What is its perimeter?

A. \(12+6\sqrt{2}\)
B. \(16+8\sqrt{2}\)
C. \(18+9\sqrt{2}\)
D. \(20+10\sqrt{2}\)
E. \(24+12\sqrt{2}\)

OA E
Solution:

Recall that the area of a right triangle is half the product of the legs of the triangle. However, since the right triangle is also isosceles, if we let x = the length of one of its legs, we have:

½ * x * x = 72

x^2 = 144

x = 12

Therefore, each of the two legs is 12, and the hypotenuse is 12 * √2 = 12√2. So the perimeter of the isosceles right triangle is 12 + 12 + 12√2 = 24 + 12√2.

Answer: E

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