A (non-degenerate) triangle with integer sides has perimeter 12. How many such non-congruent triangles are there?
Call a, b, c the sides
a + b + c = 12
And by the triangle inequality....
a + b > c
a + c > b
b + c > a
The greatest side can only = 5 and the least side has to be > 1
a b c
5 5 2
5 4 3
4 4 4
And these are the only possibilities