The area of the rectangular is \(x*2x = 32\), from which we get x = 4 (we exclude x = -4 because a side of a rectangular cannot have a negative length.

Then, using Pitagora's theorem we can find the length of the hypotenuse of the triangle, which is half of the rectangular and we get it equal to \(\sqrt(80) = 4sqrt(5)\).

Finally, the circumference of the circle is given by \(2r*\pi\) where 2r is the diameter that in this case equals \(4sqrt(5)\).

Thus, the circumference is equal to \(4\pi\sqrt(5)\). Answer B!