Question

I've tried this many times, but I keep getting a really big answer.

A rancher wants to fence in an area of 2500000 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?

Answer 1

A = a b so b = A/a

P = 2 a + 3 b

P = 2 a + 3 A/a

now A=2.5*10^6
P = 2a + 7.5*10^6/a
dP/da = 0 at in or max
dP/da = 0 = 2 -7.5*10^6/a^2
a^2 = 3.75*10^6
a = 1.936*10^3
then b = 2.5*10^6/1.936*10^3
b = 1.291*10^3
P = 2*a+3*b = 7.745*10^3