A really challengin math question for a real genius?

Question

Investigate the number of triangles generated if m lines are drawn from one corner to the opposite side and n lines are drawn from another corner to the opposite side. Find a general rule for the number of triangles generated when m and n lines are drawn from two vertices. Explain how you got this rule.

Answer 1

For m lines drawn from vertice,
there are m+1 triangles generated.
For n lines drawn from vertice,
there are n+1 triangles generated.

So, for m and n lines drawn from two vertices,
total number of triangles
= (m+1)(n+1)

Answer 2

The statement of the problem is a little ambiguous.

For example, you could mean all the triangle with a vertex at either corner, two sides generated via drawing the line segments mentioned, and a third side of the triangle on the "opposite side".

The answer for that would be m(m-1)/2 + n(n-1)/2.

Or you could mean something else.