Question

Is it possible to have a triangle with the following sides? 

1.  2 cm, 3 cm, 5 cm 
2.  3 cm, 6 cm, 7 cm 
3.  6 cm, 3 cm, 2 cm

Answer 1

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.

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(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.

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(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.