Question: If the lengths of two sides of a triangle are 5 cm and 7 cm, what is the range of possible lengths for the third side?

Options:

1. 2 cm to 12 cm
2. 3 cm to 11 cm
3. 4 cm to 10 cm
4. 5 cm to 9 cm

Correct Answer: 3 cm to 11 cm

Solution:

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 7| < third side < 5 + 7, which gives 2 < third side < 12.