Question

a perimeter of 15 cm two or more equal sides and each side a whole number of centimeters. Prove that there are only four of these triangles. You do no need to construct the triangles.

Answer 1

If two or more sides are equal, then just run through the possibilities:

1 1 13
2 2 11
3 3 9
4 4 7
5 5 5
6 6 3
7 7 1

Now, are any of these impossible? Yes, if you recall that any side must be less than the sum of the other two sides. That kicks out

1 1 13
2 2 11
3 3 9

leaving only four remaining