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

(i) We know that,

In a triangle, the sum of the length of either two sides of the triangle is always greater than the third side

The given sides of triangle in this question are:

2 cm, 3 cm and 5 cm

Now, 2 + 3 + = 5 cm

5 cm = 5 cm

Hence,

The triangle is not possible as the sum of the length of either two sides of the triangle is not greater than the third side

(ii) We know that,

In a triangle, the sum of the length of either two sides of the triangle is always greater than the third side

The given sides of triangle in this question are:

3 cm, 6 cm and 7 cm

Now, 3 + 6 = 9 cm and 9 cm > 7 cm

6 + 7 = 13 cm and, 13 cm > 3 cm

3 + 7 = 10 cm and, 10 cm > 6 cm

Hence,

The triangle is possible as the sum of the length of either two sides of the triangle is greater than the third side

(iii) We know that,

In a triangle,

The sum of the length of either two sides of the triangle is always greater than the third side

Therefore,

The given sides of triangle in this question are:

6 cm, 3 cm and 2 cm

Now,

6 + 3 = 9 cm and 9 cm > 2 cm

3 + 2 = 5 cm But, 5 cm < 6 cm

Hence,

The triangle is not possible as the sum of the length of either two sides of the triangle is not greater than the third side