The area of a right triangle is 16 square miles. one leg of the triangle is 4 miles longer than the other leg. find the length of each leg.

First, define the area of a triangle: A = 1/2bh. Let A = 16, and since it’s a right triangle, the base and the height can easily be translated to its two legs. Let one leg = x, and the other = x + 4. So this would give you the equation: 16 = .5(x)(x+4). Distribute so 16 = .5x^2 + 2x. You might want to get rid of the decimal/fraction, so multiply everything by 2 and this would give you 32 = x^2 + 4x. Recognizing that this will be a quadratic equation let x = 0 and bring everything unto one side, so 0 = x^2 + 4x - 32. Factor. 0 = (x+8)(x-4). Since a leg cannot be negative, x can only equal 4. This means that one leg is 4 and the other is 8.

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