Final answer:
A triangle can be formed by three sides, and the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the possible lengths of the third side are between 5 and 13, inclusive.
Step-by-step explanation:
A triangle can be formed by three sides, and the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, to find the possible lengths of the third side, we need to check if the sum of the given lengths is greater than the third side. In this case, the given lengths are 4 and 9. So, we can check:
- If 4 + 9 > x, where x is the third side length.
- If 9 + x > 4, where x is the third side length.
- If x + 4 > 9, where x is the third side length.
Solving these inequalities, we find that the possible lengths of the third side are between 5 and 13, inclusive.