The problem is : We are given perimeter (P) of a triangle. We need to find the number of triplet edges (a, b, c) of a triangle, so that three edges are all integer, the area and the length of the radius of the incircle and circumcircle is also an integer.

In the solution, they have an observation that : In order to exist at least a triplet satisfy the problem, 4 must be a divisor of P (perimeter) and a, b, c (three edges) must be all even.

I have proofed all a, b, c are even. But I can't figure out how 4 is a divisor of P.

Could someone help me to proof this ? Thanks in advance!!