Is it possible to construct a triangle with lengths of its sides as $4 \, cm, 3 \, cm$ and $7 \, cm$? Give reason for your answer.

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(N/A) According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.
In this case,the lengths of the sides are $4 \, cm, 3 \, cm$,and $7 \, cm$.
Calculating the sum of the two smaller sides: $4 \, cm + 3 \, cm = 7 \, cm$.
Since the sum of the two sides $(7 \, cm)$ is equal to the third side $(7 \, cm)$ and not greater than it,the triangle inequality condition is not satisfied.
Therefore,it is not possible to construct a triangle with these side lengths.

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