1. 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
As we know, According to the Triangle inequality law, the sum of lengths of any two sides of a triangle would always greater than the length of the third side. So
Verifying this inequality by taking all possible combinations, we have,
(i) 2 cm, 3 cm, 5 cm
3 + 5 > 2 ----> True
2 + 5 > 3----> True
2 + 3 > 5 ---->False
Hence the triangle is not possible.
(ii) 3 cm, 6 cm, 7 cm
3 + 6 > 7 -----> True
3 + 7 > 6 ------>True
6 + 7 > 3 ------>True
Hence, The triangle is possible.
(iii) 6 cm, 3 cm, 2 cm
6 + 3 > 2 ------>True
6 + 2 > 3 ------> True
3 + 2 > 6 ------->False
Hence triangle is not possible.