An obtuse triangle has a side length of $16,$ and a side length of $21.$ The third side length is also a positive integer. How many different possible values are there for the third side length?

Question

i got 16 but my system isn't accepting it

Answer 1

Draw and label a diagram!

If the missing side is the longest side, it is >28 (must be more than 12 + 16)

If the missing side is the shortest side, it is <4 (12 + short side < 16)