Question

Two sides of a triangle are 3 cm and 6 cm, the length of third side of triangle cannot be ______.

Options

• 2.5 cm

• 3.5 cm

• 4 cm

• 8 cm

Answer 1

Two sides of a triangle are 3 cm and 6 cm, the length of third side of triangle cannot be 2.5 cm.

Explanation:

By the triangle inequality,

The third side must be greater than |6 – 3| = 3 and less than 6 + 3 = 9. 

So any valid third side must lie between 3 and 9, not including 3 or 9.

2.5 cm < 3. 

So, it cannot be a side; 3.5 cm, 4 cm and 8 cm are all between 3 and 9.

So, they are possible.