I found this question quite intriguing.
The question was given 4 (or any generic n) triangles with the length of each side known. Is it possible to create a bigger triangle by putting these smaller triangles together? ex 2 triangles with sides (3, 4, 5) and (4, 3, 5) can be put together to create a bigger triangle (5, 5, 8).
The only method I could think of was to try all possible combinations of placing the triangles together (by joining common sides) and see if the result is a valid triangle.