If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.

We know that,

The sum of any two sides of a triangle is always greater than the third side.

⇒ Third side < 13 + 8

⇒ Third side < 21 cm.

The difference of any two sides of a triangle is always less than the third side.

⇒ Third side > 13 - 8

⇒ Third side > 5 cm.

Thus, length of third side is between 5 cm and 21 cm.

Given, a is less than b.

Hence, a = 5 cm and b = 21 cm.