Question 907533
x the shorter leg
x^2 + (x+1)^2 = 25
x^2 + x^2 + 2x+ 1 = 25
2x^2 + 2x - 24 = 0 
x^2 + x - 12 = 0
(x+4)(x-3)= 0 (Tossing out the negative solution for unit measure)
x= 3, the shorter leg.  The longer leg is 4 {{{3+1}}}
and..checking
9 + 16 = 25