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

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Question 105792: The length of one leg of a right triangle is 24ft. The length of the other leg is 16 ft shorter than the hypotenuse. Find the length of the hypotenuse and the other leg. I believe the formula should be 24 squared + c squared - 16 = c squared but I can't get the equation to work without having a negative number. What am I doing wrong.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The length of one leg of a right triangle is 24ft. The length of the other leg is 16 ft shorter than the hypotenuse. Find the length of the hypotenuse and the other leg. I believe the formula should be 24 squared + c squared - 16 = c squared but I can't get the equation to work without having a negative number. What am I doing wrong.
:
Well, that's almost the way to do it,
you should have (c-16)^2, not c^2 - 16

:
Using c^2 = a^2 + b^2
we have:
a = 24; b = (c-16)
Therefore
c^2 = 24^2 + (c-16)^2
:
c^2 = 576 + c^2 - 32x + 256
:
Let's put the variables on the left and numbers on the right
c^2 - c^2 + 32c = 576 + 256
:
32c = 832
:
c = 26 ft is the hypotenuse
then
b = 26 - 16
b = 10 ft
:
Check our solution:
24^2 + 10^2 = 26^2
576 + 100 = 676