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Need a geometry explaination please

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Can someone offer me an explanation? Or confirm that I'm not crazy. I'm good with either.


"The Sum of any two sides (of a triangle) must be greater than the third side"


Examples given:

3, 4, 5

4, 5, 8

4, 6, 9


In the teacher's manual there is one set of numbers marked as not a triangle, though it meets the above rule. Why?


The set is:

15, 6, 12


Why is this not a triangle?


15 is less than 18 (6+12)

6 is less than 27 (15+12)

12 is less than 21 (15+6)


It meets the rules. Why is it not a triangle? (Or maybe the TM is wrong, but it isn't listed as a known correction on the company website.)

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