Non-congruent triangles

Question

Suppose you are given a rectangular picture frame with a length of 10 inches and width of 6 inches. If you break the frame apart into 4 pieces (2 pieces with a length of 10 inches and 2 pieces with a length of 6 inches), how many non-congruent triangles can be formed by using 3 of the 4 pieces? Pieces may be reused from one triangle to the next.

The answer I came up with is 2 non-congruent triangles, because you can have a triangle with sides of 6, 6, and 10 AND a second triangle with sides of 6, 10, 10. Any other combination of numbers would be a repeated? Am I right?

Thanks for your help.

Answer 1

You're right. I can't think of anything else either