A botanical display is to be constructed as a rectangular region with a river as one side and a sidewalk 2 meters wide along the inside edges of the other three sides. (See Fig. 1.) The area for the plants must be 800 square meters. Find the outside dimensions of the region that minimizes the area of the sidewalk (and hence, minimizes the amount of concrete needed for the sidewalk).

Sidewalk Plants River X x-4 Figure 1 A botanical display. y-2 SE y