If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube ?
Options:
A . 6$$\sqrt 3 $$ cm
B . 12 cm
C . 15 cm
D . 12$$\sqrt 3 $$ cm
Answer: Option D 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
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