Given no shape constraints all answers except A are possible.
A right Triangle will have the smallest area to perimeter ratio and solving the quadratic for a triangle base that results in an area and perimeter of 12 yields only complex roots. Given that all other shapes will have a larger A to P ratio answer A is impossible.
Answers B,C, and D may all be achieved by assuming a rectangle and setting up two equations for each answer. 2(L)+2(W)=Answer and (L)(W)=12.
Answer B yields a 3x4 Blanket.
Answer C yields a sqrt(3/2) by 12/(sqrt(3/2)) blanket.
Answer D yields a sqrt(9/2) by 12/(sqrt(9/2) blanket.
As there is nothing that indicates the blanket dimensions must be integers they are all equally correct.
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.