suppose that you have 800ft of fencing. you are to construct a rectangular corral which is divided into two pieces. what are the dimensions that give the largest possible areas?

Answer 1

The way to divide a rectangle in two pieces using minimum fence materials is to build a third fence segment having the width dimension, W,in the middle somewhere. The rectangle length L is then given by
3W + 2L = 800, so
L = 400 - 3/2 W

Area = L*W = 400W -(3/2)W^2
dA/dW = 0 = 400 - 3W
W = 133 1/3 ft ; L = 200
gives maximum area