Question 374530
A suggestion:  Let x  = the unknown leg, and y = the hypotenuse.  Then 
from the perimeter condition, x+y+12 = 60, or x+y = 48, or y = 48 - x.
From the right-triangle condition, use the Pythagorean identity : {{{12^2 + x^2 = y^2}}}.
Substituting, we get {{{144 + x^2 = (48-x)^2}}}.  Now see if there will be any progress...