Explanation

From the Third Side Rule, any side of a triangle must be greater than the difference of the other two sides and less than their sum. Since 9 – 7 = 2 and 9 + 7 = 16, the unknown third side must be between 2 and 16, not inclusive.

To get the lower boundary for the perimeter, add the lower boundary of the third side to the other two sides: 2 + 7 + 9 = 18. To get the upper boundary for the perimeter, add the upper boundary for the third side to the other two sides: 16 + 7 + 9 = 32. Thus, p must be between 18 and 32, not inclusive—in other words, 18 < p < 32.