All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are congruent.)
Only 1 triangle is possible, and its side lengths are 1-1-1.
Any other triangle with that perimeter won't have integer sides.
.
+570 
