let 'x' represent the length of the shorter leg, then 'x+12' represents the hypotenuse and 'x+2' represents the longer leg

since this is a right triangle:

hypotenuse^2 = short-leg^2 + long-leg^2

(x+12)^2 = x^2 + (x+2)^2

solving for 'x' we have a positive value of x=25.49

by rounding 'x', we take the shorter leg to be equal to 25.5

25.5 + 12 = 37.5

25.5 + 2 = 27.5

the lengths of the sides are approximately 25.5, 27.5 and 37.5 inches