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Is it possible to have a triangle with the following sides?
$(i).\ 2 cm,\ 3 cm,\ 5 cm$
$(ii).\ 3 cm,\ 6 cm,\ 7 cm$
$(iii).\ 6 cm,\ 3 cm,\ 2 cm$
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.
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