Let x = the shorter leg. Then the longer leg = x + 1.
Using the Pythagorean Theorem you get:
x2 + ( x+ 1 )2 = 52. *****. this is the answer to the question.
The following is how you would find x.
x2 + x2 + 2x + 1 = 25. ( foil out (x + 1)2 )
2x2 + 2x - 24 = 0. ( combine like terms and bring everything to one side)
x2 + x - 12 = 0 ( divide both sides by 2)
( x + 4 ) ( x - 3 ) = 0. ( factor )
x = -4 or x = 3
Since you can not have a negative length for a side, the answer has to be x = 3