SOLUTION: "Find the length of the legs of a right triangle having a perimeter of 56m if the hypotenuse is 25m." Thanks for the help!

Algebra ->  Triangles -> SOLUTION: "Find the length of the legs of a right triangle having a perimeter of 56m if the hypotenuse is 25m." Thanks for the help!      Log On


   

Question 43532: "Find the length of the legs of a right triangle having a perimeter of 56m if the hypotenuse is 25m." Thanks for the help!
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
leg = a
other leg = b
a+%2B+b+%2B+25+=+56
a+%2B+b+=+31
b+=+31+-+a
Next:
a%5E2+%2B+b%5E2+=+c%5E2
a%5E2+%2B+b%5E2+=+625
Plug:
a%5E2+%2B+%2831+-+a%29%5E2+=+625
a%5E2+%2B+961+-+62a+%2B+a%5E2+=+625
2a%5E2+-+62a+%2B+336+=+0
a%5E2+-+31a+%2B+168+=+0
%28a+-+24%29%28a+-+7%29+=+0
a+=+24 and a+=+7
Plug:
b+=+31+-+a
b+=+31+-+24 and b+=+31+-+7
b+=+7 and b+=+24
The leg's lengths: 7m and 24m