SOLUTION: The hypotenuse of a right triangle is 9 feet long. One leg is 2 feet longer than the other. Find the length of the legs. What is the shorter leg? The longer leg?

Question 816954: The hypotenuse of a right triangle is 9 feet long. One leg is 2 feet longer than the other. Find the length of the legs. What is the shorter leg? The longer leg?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
h = sqrt( aa + bb )
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h = 9
a = b + 2
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h = sqrt( aa + bb )
9 = sqrt( (b + 2)(b + 2) + bb )
81 = (b + 2)(b + 2) + bb
81 = bb + 4b + 4 + bb
2b^2 + 4b - 77 = 0
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the above quadratic equation is in standard form, with a=2, b=4, and c=-77
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to solve the quadratic equation, plug this:
2 4 -77
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
b = 5.28490254
b = -7.28490254
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the negative root doesn't make sense for a length, so use the positive root:
b = 5.28490254
a = 7.28490254
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Answer:
the length of the legs is:
a = 7.28490254 ft
b = 5.28490254 ft
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