SOLUTION: The hypotenuse of a right triangle is 26 feet long. One leg is 14 feet longer than the other. Find the length of the shorter leg. ___ ft long. Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The hypotenuse of a right triangle is 26 feet long. One leg is 14 feet longer than the other. Find the length of the shorter leg. ___ ft long. Thank you       Log On


   

Question 41039: The hypotenuse of a right triangle is 26 feet long. One leg is 14 feet longer than the other. Find the length of the shorter leg.
___ ft long.
Thank you
Found 2 solutions by Nate, checkley71:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Shorter Leg = s
Longer Leg = s + 14
Theorm:
a%5E2+%2B+b%5E2+=+c%5E2
%28s%29%5E2+%2B+%28s+%2B+14%29%5E2+=+26%5E2
s%5E2+%2B+s%5E2+%2B+28s+%2B+196+=+676
2s%5E2+%2B+28s+-+480+=+0
s%5E2+%2B+14s+-+240+=+0
%28s+-+10%29%28s+%2B+24%29+=+0
s+=+10 or s+=+-24
Side can not be negative.
s+=+10

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X~2+(X+14)~2=27~2 OR X~2+X~2+28X+196=27*27 OR 2X~2+28+196-729=0 OR
2X~2+28X-533=0 OR (2X+41)(X-13)=0 OR X=-41/2 & X=13