Even A is correct. It does not specify width of border or whether corners are needed. It does not specify a uniform border. There certainly is a border solution whose total area is 12 square units.
It certainly sounds reasonable that given infinite possibilities there could be some irregular shape out there whose area and perimeter both equal 12 units. It would be interesting to see a mathematical proof one way or the other. It would also be interesting to see if I could follow said proof :-)