# 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$

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Given: Sides:
$(i).\ 2 cm,\ 3 cm,\ 5 cm$

$(ii).\ 3 cm,\ 6 cm,\ 7 cm$

$(iii).\ 6 cm,\ 3 cm,\ 2 cm$

To do: To check whether it is possible to have a triangle with the given sides.

Solution:

In a triangle, the sum of its two sides is always greater than the third side of the triangle. Now we will check the given sides by using this criterion:

$(i).\ 2+3>5$, No

$2+5>3$,  yes

$3+5>2$, yes

This triangle is not possible.

$(ii).\ 3+6>7$,  yes

$6+7>3$,   yes

$3+7>6$,   yes

This triangle is possible.

$(iii).\ 6+3>2$,  yes

$6+2>3$, yes

$2+3>6$, no

This triangle is not possible.
Updated on 10-Oct-2022 13:34:22