Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm    (ii) 3 cm, 6 cm, 7 cm
(iii) 6 cm, 3 cm, 2 cm

Solution:

This problem is based on the triangle inequality property which states that if the sum of lengths of any two sides of a triangle is greater than the third side, then it is possible to draw a triangle.

By using this property, we will be taking the sum of any two sides of a triangle and check whether it is greater than the third side or not.

(i) 2 + 3 > 5 ⇒ No

3 + 5 > 2 ⇒Yes

5 + 2 > 3 ⇒ Yes

No, the triangle is not possible

(ii) 3 + 6 > 7 ⇒ yes

6 + 7 > 3 ⇒ yes

7 + 3 > 3 ⇒ yes

Yes, the triangle is possible

(iii) 6 + 3 > 2 ⇒ yes

3 + 2 > 6 ⇒ No

2 + 6 > 3 ⇒ Yes

No, the triangle is not possible

Useful Tip: Whenever you encounter problems of this kind, it is best to think of the property based on the sum of lengths of any two sides of a triangle

☛ Check: Class 7 Maths NCERT Solutions Chapter 6

Video Solution:

Is it possible to have a triangle with the following sides? (i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm (iii) 6 cm, 3 cm, 2 cm

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.4 Question 1

Summary:

It is possible to have a triangle with the following sides (ii) 3 cm, 6 cm, 7 cm whereas, it is not possible to have a triangle with the following sides (i) 2 cm, 3 cm, 5 cm, (iii) 6 cm, 3 cm, 2 cm

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