if n is an integer and 3<n<8 , how many different triangles are there with side lengths of 3, 8, and n?
The sum of any two sides of a triangle must be greater than the third side, so
3+n>8 AND n+8>3 AND 3+8>n
n> 5 and n> -5 and n<11
so n>5 and n< 11
so n could be 6,7,8,9, and 10 which would make the answer
5 such triangles