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Question:

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

A 12.6
explanation

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 b2 = 24, so 2/3 * 3/2 b2= and b2 = 16. b = √16 = 4 and h = 3 × 4 = 12. The longest side of a right triangle is the hypotenuse. Using the Pythagorean theorem, leg2+ leg2= hypotenuse 2, so 42+ 122= c2 and 16 + 144 = c2. Therefore, 160 = c2 and c = √160 = 12.6.