The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the squareis:

The correct option is C.

 Let the length of edge of cube is $$a$$. And the length of side of square is $$b$$.

 There are 12 edges in cube. So, 

  $$12a=2b$$

 $$\Rightarrow$$ $$a=\frac{b}{6}$$ .....(1)

 Again from question, vol of cube = area of square 

       $$\Rightarrow$$ $$a^{3}=b^{2}$$

        $$\Rightarrow$$ $$(\frac{1}{6})^{3}$$ $$\times$$ $$b^{3}$$ = $$b^{2}$$    (From equation 1)

           b = 216