The vertices of an equilateral triangle lie on the hyperbola xy=1, and a vertex of this hyperbola is the centroid of the triangle. What is the square of the area of the triangle?<spanclass=′latex−bold′>(A)</span> 48<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 108<spanclass=′latex−bold′>(D)</span> 120<spanclass=′latex−bold′>(E)</span> 169