Chapter 3, Problem 18RE

Repeat Exercise 17, with the sidewalk on the inside of all four sides. In this case, the $800$-square- meter planted region has dimensions $x-4$ meters by $y-4$ meters.

Minimizing Area 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 plant 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).