An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200m running track. Find the dimension that will make the area of the rectangular as large as possible.

Answer 1

Perimeter=2L + PI*W think about that.

Area=LW+PI*w^2/4

L from the first equation is (Perimeter-PI/W)1/2

Put that value of L in the second area equation, take the derivative of area with respect to W, set to zero, and solve for W. Then go back to the perimeter equation and solve for L.