If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube ?

Solution (By Examveda Team)

Since a cube has 4 diagonals, we have :
Length of a diagonal
$$\eqalign{ & = \left( {\frac{{12}}{4}} \right)cm \cr & = 3\,cm \cr} $$
Let the length of each edge of the cube be a cm
Then,
$$\eqalign{ & \sqrt 3 a = 3 \cr & or,a = \sqrt 3 \cr} $$
∴ Total length of the edges of the cube = $$12\sqrt 3\, $$ cm