The measures of two sides are given. Between what two numbers must the third side fall. 23 and 14. Using n as your variable

Solution:
1. Given:
- Two sides: 23 and 14
- Third side: n

2. Use the triangle inequality theorem. For any triangle with sides a, b, and c, the following must hold:
- a + b > c
- a + c > b
- b + c > a

3. Apply the triangle inequality to the given sides:
- 23 + 14 > n
- 23 + n > 14
- 14 + n > 23

4. Simplify each inequality:
- 37 > n or n < 37
- n > 14 - 23 simplifies to n > -9, which is unnecessary as side lengths must be positive.
- n > 9

5. Combine the inequalities:
- Since n > 9 and n < 37, the length of the third side must be:
9 < n < 37