Question 38560: I need your help to solve this problem and also what are the steps to solve this problem.
The length of a hypotenuse of a right triangle is 2 feet more than the longer leg. The length of the longer leg is 7 feet more than the lenth of the shorter leg. Find the number of feet in length of each side of the right triangle.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! For every right triangle, a^2 + b^2 = c^2...
Let x = the length of the shorter leg.
Thus x + 7 is the longer leg and
x + 9 is the length of the hypotenuse...
So substituting into the Pythagorean Theorem, we have
x^2 + (x + 7)^2 = (x + 9)^2
x^2 + (x^2 + 14x + 49) = x^2 + 18x + 81
now collect like terms and solve for x
2x^2 + 14x + 49 = x^2 + 18x + 81
x^2 - 4x - 32 = 0
(x - 8)(x + 4) = 0
x = 8 and x = -4
but distances cannot be negative, so
x = 8
The other sides must be 15 and 17.
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