Two sides of an obtuse triangle are 16 and 21. how many possible lengths are there for the third side, if it is a positive integer?

If the triangle is obtuse, then the sum of the squares of the 2 shortest sides (16^2 + 21^2 = 697) has to be less than the square of the longest side.

So, the longest side must be greater than the sq root of 697 AND less than the sum of the 2 shortest sides (37)

Source:
http://www.1728.org/triantest.htm

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It would be 18 cm