Triangle Inequality
Geometry
Level
3
Consider triangles having integer sides such that no side is greater than 4 units . How many such triangles are possible?
The answer is 13.
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1 solution
Max length 1: (1,1,1) -- 1 triangle
Max length 2: (2,2,2), (2,2,1) -- 2 triangles
Max length 3: (3,3,3), (3,3,2), (3,3,1), (3,2,2) -- 4 triangles
Max length 4: (4,4,4), (4,4,3), (4,4,2), (4,4,1), (4,3,3), (4,3,2) -- 6 triangles
Total: 1 + 2 + 4 + 6 = 13 triangles (non-degenerate)