SOLUTION: the hypotenuse of a right triangle is 2 ft. longer than one leg and 4 ft. longer than the other leg. what are the dimensions of this triangle?

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Question 1005336: the hypotenuse of a right triangle is 2 ft. longer than one leg and 4 ft. longer than the other leg. what are the dimensions of this triangle?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x = the length of the hypotenuse, in feet.

Then the legs are (x-2) ft and (x-4) ft,

and you have a quadratic equation

x-2%29%5E2 + %28x-4%29%5E2 = x%5E2.

Simplify, and you will get

x%5E2+-+12x+%2B+20 = 0.

There are two roots, 10 and 2.

The smaller doesn't fit. The greater does work.

Answer. 10 ft.