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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?

 May 28, 2020
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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?

 May 28, 2020

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