The dimensions of a rectangle R are a and b, a<b. It is required to obtain a rectangle with dimensions x and y, x<a, y<a, so that its perimeter is one-third that of R, and its area is one-third that of R. The number of such (different) rectangles is:<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>infinitely many