SOLUTION: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.

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Question 110820: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
If the shorter leg is x, then the longer leg is twice that plus 4. So the two legs are:
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x and
2x + 4
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In a right triangle the base can be one leg and this makes the other leg the height.
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The equation for the area of a triangle is:
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For this problem A = 120 sq inches, b = x inches, and h = 2x + 4 inches.
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Substituting these values into the area equation results in:
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Multiplying out the right side results in:
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Transpose the equation (switch sides) to get:
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Get rid of the 120 on the right side by subtracting 120 from both sides to get:
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Notice that the left side of the equation factors and the result is:
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This equation will be true if either of the two factors on the left side is zero because
multiplication by zero results in zero ... making the left side equal to the zero on the
right side.
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So, one at a time, set each factor equal to zero.
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First
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Solve this by subtracting 12 from each side to get:
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This can't be the answer because having a leg equal to a negative value makes no sense.
So proceed to set the second factor equal to zero:
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Solve this by adding 10 to each side:
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This solution tells you that the short leg is 10 inches long. And this means that the
longer leg is 2*10 + 4 = 20 + 4 = 24 inches.
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So the two legs are 10 inches and 24 inches.
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Check:
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The area has to be sq inches. This checks.
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Hope this helps you to understand the problem and how to solve it.
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