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

Answers (1)

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.

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