The maximum side can be no less than 6 when all three sides
are equal in length.
1. When the maximum side is 6, all three sides are 6.
That's 1 way.
2. When the maximum side is 7, the other two sides must have
sum 11, and be 7 or less, so there are 2 possibilities for
the other two sides, either 4 and 7 or 5 and 6.
That's 2 more ways.
3. When the maximum side is 8, the other two sides must have
sum 10, and be 8 or less, so there are 4 possibilities for
the other two sides, 2 and 8, 3 and 7, 4 and 6, or 5 and 5.
That's 4 more ways.
Total: 1+2+4 = 7 ways.
Edwin
