Question

If two sides of a triangle are given as 10 cm and 8 cm, then which of the following can be the length of the third side to construct that triangle?

• A. 2 cm
• B. 19 cm
• C. 3 cm
• D. Any length less than 2 cm

Answer 1

The correct option is C 3 cm

To construct a unique triangle with the three sides, it must satisfy the sides' constraint which is:

"Sum of any two sides of a triangle must be greater than the third side".

Here, in options a, b and d, this constriant is not being satisfied.

In option a:
8 cm + 2 cm is equal to 10 cm and not greater than 10 cm.
In option b:
8 cm + 10 cm is less than 19 cm.
In option d:
The third side cannot be less that 2 cm, because 8 + third side shpuld be greater that 10 cm.

Therefore, option c is correct where
8 cm + 3 cm > 10 cm,
8 cm + 10 cm > 3 cm, and
10 cm + 3 cm > 8 cm.