How many non-congruent triangles are there with sides of integer length having at least one side of length six units and having no side longer than six units?

Guest May 28, 2020

#1**0 **

One side of the triangle must be 6.

Then, if the second side is also 6, the third side can be either 6, 5, 4, 3, 2, or 1 -- 6 possibilities.

If the second side is 5, the third side can be either 5, 4, 3, or 2 -- 4 possibilities.

If the second side is 4, the third side can be either 4 or 3 -- 2 possibilities.

The second side cannot be shorted than 4.

Did I miss any?

geno3141 May 28, 2020