Question

Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.

There are ___(number) different triangles he can create that fit these conditions.

Of these triangles, there are ___(number) isosceles, ___(number) scalene, and ___(number) equilateral.