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.