SOLUTION: the hypotenuse of a right triangle is 1 inch longer than the longer leg. the shorter leg is 7 inches shorter than the longer leg. find the length of the hypotenuse.

Question 797192: the hypotenuse of a right triangle is 1 inch longer than the longer leg. the shorter leg is 7 inches shorter than the longer leg. find the length of the hypotenuse.
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Longer leg = x
Shorter leg = x - 7
Hypotenuse = 1 + x
x^2 + (x - 7)^2 = (1 + x)^2
x^2 + x^2 - 14x + 49 = 1 + 2x + x^2
Collect like terms:
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x - 4 = 0
x = 4 (no answer as shorter leg = - number)
x - 12 = 0
x = 12
Longer leg = 12 inches
Shorter leg = 5 inches
Hypotenuse = 13 inches.
Hope this helps.
:-)
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