A triangle has three different integer side lengths and a perimeter of 20 units. What is the maximum length of any one side?

The maximum side must be < 20/2 = 10, because the sum of the 2 shorter sides must be > than the longest side.

So, I would say 9 would the maximum side. The other 2 sides could be:

8 and 3

7 and 4

6 and 5 in that they all must be whole integers and different from each other.