Explanation:

- In a triangle, the length of any side must be less than the sum and more than the difference of the other two sides (Triangle Inequality Theorem).

- Here, the two known sides are 5 cm and 8 cm.

- So, the possible range for the third side (x) is:

8 - 5 < x < 8 + 5

3 < x < 13

- Looking at the options:

- Option 1: 3 cm , not possible as it equals the lower limit.

- Option 2: 14 cm , not possible as it exceeds the upper limit.

- Option 3: 2 cm , not possible as it is less than the lower limit.

- Option 4: 4 cm , possible as it lies between 3 and 13.

Correct Answer: Option 4 - 4 cm