The area of a rhombus is $$24m^{2}$$ and the length of one of its diagonals is 8 m. The length of
each side of the rhombus will be:

The correct option is A.

In a Rhombus diagonals bisect each other at right angle. Let diagonal AC= 8m. 

                     Area of rhombus = $$\frac{1}{2}$$ $$d_{1}d_{2}$$ 

   $$\Rightarrow$$  24 = $$\frac{1}{2}$$ 8$$\times d_{2}$$

                           $$d_{2}$$ = 6m 

AO=4m and DO = 3 m  so, in $$\triangle$$AOD , $$AD^{2}=AO^{2}+DO^{2}$$

                                                           $$\Rightarrow$$ AD = 5m