SOLUTION: The length of one leg of a right triangle is 24 ft. The length of the other leg is 16 ft. shorter than the hypotenuse. Find the length of the hypotenuse and the other leg. Would

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: The length of one leg of a right triangle is 24 ft. The length of the other leg is 16 ft. shorter than the hypotenuse. Find the length of the hypotenuse and the other leg. Would      Log On

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Question 57915: The length of one leg of a right triangle is 24 ft. The length of the other leg is 16 ft. shorter than the hypotenuse. Find the length of the hypotenuse and the other leg. Would it be (x-16)^2+24^2=x?? If it is, I'm not quite sure how to solve that.
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
The length of one leg of a right triangle is 24 ft. The length of the other leg is 16 ft. shorter than the hypotenuse. Find the length of the hypotenuse and the other leg.
Let the hypotenuse=x
the length of one leg=24 ft
the length of the other=x-16
The pythagorean theorem is: hypotenuse^2=leg^2+other leg^2
:
x%5E2=24%5E2%2B%28x-16%29%5E2
x%5E2=576%2Bx%5E2-32x%2B256
x%5E2=x%5E2-32x%2B832
-x%5E2%2Bx%5E2=-x%5E2%2Bx%5E2-32x%2B832
0=-32x%2B832
-832%2B0=-32x%2B832-832
-832=-32x
-832%2F-32=-32x%2F-32
26=x
The hypotenuse:x=26 ft.
The other leg:x-16=26-16=10 ft.
:
Check:
26%5E2=24%5E2%2B10%5E2
676=576%2B100
676=676 Feels good to be right!!!
Happy Calculating!!!