12 cm
The solution to this problem requires the Pythagorean theorem which is
a^2 + b^2 = c^2
where
a,b = legs of the right triangle
c = hypotenuse of right triangle
Let's substitute the known values into the equation and solve
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
So the length of the 2nd leg is 12 cm.
