SOLUTION: the hypotenuse of right triangle is 24 ft long.the length of one leg is 18 ft more than the other. find the lengths of the legs

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Question 374731: the hypotenuse of right triangle is 24 ft long.the length of one leg is 18 ft more than the other. find the lengths of the legs
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let one leg's length be L.
Use the Pythagorean theorem,
L%5E2%2B%28L%2B18%29%5E2=24%5E2
L%5E2%2BL%5E2%2B36L%2B324=576
2L%5E2%2B36L-252=0
L%5E2%2B18L-126=0
.
.
L%5E2%2B18L%2B81-126=81
%28L%2B9%29%5E2=81%2B126
%28L%2B9%29%5E2=207
L%2B9=0+%2B-+sqrt%28207%29
L=-9+%2B-+sqrt%28207%29
Only the positive value makes sense for this problem.
highlight%28L=-9%2Bsqrt%28207%29%29
.
.
highlight%28L%2B18=9%2Bsqrt%28207%29%29