Homework SourseA rancher wants to fence in an area of 2000000 square feet i
A rancher wants to fence in an area of 2000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Solution
Set the two sides of the rectangular field to be X and Y Then, XY = 1000000 let Y = 1000000/X Then, Total length of fence L(X) = 3X + 2Y = 3X + 2000000/X L\'(X) = 3 - 2000000/ (X^2) when L\'(X) = 0 there is a minimum value so, X = sqrt(2000000/3) = 1000 sqrt(2/3) The shortest Length of fence = L(X) = 3X + 2000000 / X = 2000 sqrt(6) ~= 4898.98
