Let x and y are the legs (the dimensions of the legs, I mean).


Then you have these to equations

x + y + 50 = 112,    (1)    (perimeter)

 = 50.        (2)    (hypotenuse; Pythagorean equation)

Or, equivalently,

x + y = 62,          (1')

 = 2500.       (2')

From equation (1') express y = 62-x and substitute it into equation (2'). You will get

 = 2500,

 = 2500,

 = 0,

 = 0.

Use quadratic formula and complete the solution on your own.