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Question:

A right triangle has an area of 24 feet. If one leg is 3 times as long as the other, what is the length of the longest side?

A
12.6

Explaination

The area of a triangle is 1/2 bh. Let b represent the length of one leg. Then h = 3b so the area is 1/2 bh =1/2 * b * 3b =3/2 b^{2}=24, so 2/3 * 3/2 b^{2}= and b^{2} = 16. b = √16 = 4 and h = 3 × 4 = 12. The longest side of a right triangle is the hypotenuse. Using the Pythagorean theorem, leg^{2}+ leg^{2}= hypotenuse ^{2}, so 4^{2}+ 12^{2}= c^{2} and 16 + 144 = c^{2}. Therefore, 160 = c^{2}and c = √160 = 12.6.