Let the enclosure dimensions be  x = length, y = width, so the area is xy = 4000 square meters.


Then you have a rectangle of the perimeter of 2x + 2y plus two additional fence parts of the length y. 


The total length of the fencing with two additional fence parts is 2x + 4y meters.


Thus you need to minimize  2x + 4y  under the condition  xy = 4000.


Express y = 4000/x  and substitute it into  2x + 4y.  Then you will get that the function to minimize is  .


To find a minimum, differentiate the function over x and equate to zero. 


So, the equation for the minimum is


 -  = 0,   or   = 2  ====>   =  = 8000  ====>  x =  = .


Thus the optimal dimensions are: the length =  = 89.44 m  and

                                 the width =  =  =  = 44.72 m.


Check.  89.44*44.72 = 4000 square meters.   ! Correct !