Question

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

• A. a=5 cm and b=13 cm
• B. a=8 cm and b=21 cm
• C. a=21 cm and b=5 cm
• D. a=5 cm and b=21 cm

Answer 1

The correct option is D a=5 cm and b=21 cm

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

Third side < 13+8 =21 cm
The difference between any two sides of the triangle is always less than the third side of the triangle.

Third side > 13-8 =5 cm.

Therefore, the length of the third side is between 5 cm and 21 cm, respectively.

The value of a =5 cm and b= 21cm.