Question

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.

Answer 1

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Define x:
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Let one of the leg be x and the other leg is x + 4.

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Formula:
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Area of triangle = 1/2 x base x height

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Find x:
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16 = 1/2 (x) (x+4)

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Multiply by 2 on both sides:
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32 = x(x+4)

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Apply distributive property:
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32 = x² + 4x

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Subtract 32 from both sides:
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x² + 4x - 32 = 0

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Factorise:
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(x - 4)(x + 8) = 0
x = 4 or x = -8 (rejected, length cannot be negative)

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Find the length of the legs:
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One leg = x = 4 miles
The other leg = x + 4 = 4 + 4 = 8 miles

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Answer: The 2 legs are 4 miles  and 8 miles.
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Answer 2

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.