easy way

since x is not longest side, x should be between 7 (20-13) and 20 not inclusive. 

since area is 66 and area for triangle is 1/2 * b * h, b*h should be 132, if b is integer, h should be integer as well, 132=11*12=11*3*2*2, then b should be 11 or 12, 12 doesn't work (proof is easy), so b is 11, which is x. 

i did it in 1 min ;)