The difference between the lengths of any two sides of a triangle is smaller than the length of third side. State whether the statement is true or false.

Solution:

Given, the difference between the lengths of any two sides of a triangle is smaller than the length of the third side.

We have to determine if the given statement is true or false.

Consider a triangle ABC with sides AB = 6 cm, BC = 10 cm and AC = 4 cm.

We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Sum of two sides = 6 + 10

= 16 cm

We know that the third side must be greater than the difference between two sides and less than the sum of two sides.

Difference of two sides = 10 - 6

= 4 cm

Therefore, the third side must be greater than the difference between two sides.

✦ Try This: Sum of two sides of a triangle is lesser than the third side. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 72

The difference between the lengths of any two sides of a triangle is smaller than the length of third side. State whether the statement is true or false.

Summary:

The given statement,”The difference between the lengths of any two sides of a triangle is smaller than the length of third side” is true.

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