Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.

(B) Let the length of the edge of the cube be $a$.
The formula for the length of the diagonal of a cube is $\sqrt{3} a$.
Given that the length of the diagonal of the cube is $6 \sqrt{3} \, \text{cm}$.
Equating the two,we get $\sqrt{3} a = 6 \sqrt{3}$.
Dividing both sides by $\sqrt{3}$,we get $a = 6 \, \text{cm}$.
Therefore,the length of the edge of the cube is $6 \, \text{cm}$,not $3 \, \text{cm}$.
Hence,the given statement is False.