Just for the sake of amusement, I will hint and direct people towards the right path. Looking at the solution link (and even the illustration), there is a thick green outline and a triangle inside. Taking that into account, one triangle in the answer accounts actually for 3 triangles (the thick green line alone, the yellow triangle alone without the thick green line, and the whole triangle which the answer uses). So, there are at least 132 legitimate triangles. Cheers mates.