The sides of a triangle are expressed in natural numbers. How long can the third side be if the lengths

The sides of a triangle are expressed in natural numbers. How long can the third side be if the lengths of the other two sides are 9 cm and 7 cm, and the perimeter is less than 29 cm?

To solve this problem, recall the condition for the existence of a triangle. For a triangle, the sum of the other two sides must be greater than the third side.
9 + 7> x;
16> x.
7 + x> 9
x> 9-7
x> 2.
The third side is less than 16 centimeters and more than two.
Perimeter less than 29.
We get the inequality
16 + x <29;
x <29-16;
2 cm <x <13 cm.
Answer: 2 cm <x <13 cm.