Tim wants to fence in an area of 3000000 square feet in a rectangular field, then divide it in half with a fence down the middle parallel to one side. Shortest length of fence the rancher can use?

Answer 1

W=3*10⁶/L (Note the unit of 3 is million square feet)

F = 2(L + W) + W

F = 2L + 3W = 2L + (9*106/L)

dF/dL = 2 - (9*10⁶/L²)

At the minimum 2L² = 9*10⁶ and L = 3*10³/√2 =(3/2)*10³√2 feet

W = 10³√2 feet

and you can get F the number of feet of fence as 2L + 3W