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
In a triangle, the sum of the lengths of either two sides is always greater than the third side.
(i) Given that, the sides of the triangle are 2 cm, 3 cm, 5 cm.
It can be observed that,
2 + 3 = 5 cm
However, 5 cm = 5 cm
Hence, this triangle is not possible.
(ii) Given that, the sides of the triangle are 3 cm, 6 cm, 7 cm.
Here, 3 + 6 = 9 cm > 7 cm
6 + 7 = 13 cm > 3 cm
3 + 7 = 10 cm > 6 cm
Hence, this triangle is possible.
(iii) Given that, the sides of the triangle are 6 cm, 3 cm, 2 cm.
Here, 6 + 3 = 9 cm > 2 cm
However, 3 + 2 = 5 cm < 6 cm
Hence, this triangle is not possible.