Question

Two sides of a triangle are as follows: 2 centimeters and 5 centimeters. Describe the possible lengths of the third side

Answer 1

3cm < Third side < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values of third side are

4cm, 5cm,6cm

Explanation:

This question can be solved using given by Triangle Inequality Theorem Given below.

• Sum of two sides is always greater than value of third side
• Difference of two sides is always less than value of third side

Given two sides are 2cm, 5cm

Sum of two sides = (2+5)cm = 7 cm

Difference of two sides = (5-2) = 3 cm

Let the third side be X

thus according to Triangle Inequality Theorem

X < Sum of two sides of given triangle

X < 7cm -----1

X > Difference of two sides

X > 3cm ----1

combining expression 1 and 2 we have

3cm < X < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values are

4c, 5cm,6c