hello, to do this exercise, we need to know about the property of the existence of a triangle.
I will call the sides by "a" = 8 inches, "b" = 10 inches and "c" = unknown side
to exist, it has 2 rules:
- the lenght of one side must be less than the sum of the other two sides.

- the third size must be bigger than the absolute value of the difference of the other two sides.

If we put it in one inequation, we have:

Replacing "a" and "b" with the values we have:
[tex]\begin{gathered} |8-10|\text{ < c < 8+10} \\ |-2|\text{ < c < 18} \\ 2
So, the lenght of the third size can be any value between 2 and 18.
Solution: {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20}.