A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence? 4000 ft is the smaller value that I found

what's is the larger value in ft?

Let the length of the base = b. Notice there is 2 b's in the rectangle.

Let the height = h. Notice there are 3 h's in the rectangle.

The question is asking how to minimize the cost of the fence. This is equivalent to asking how to minimize the perimeter.

Step-by-step explanation:

A = bh

A / b = h

P = 2b + 3h

P = 2b + 3(A / b)

P = 2b + 3Ab⁻¹

dP/db = 2 - 3Ab⁻² --- {Let dP/db = 0 to find the maximum}

3Ab⁻² = 2

b = √[3A / 2]

A = bh

h = A / √[3A / 2]

b = 6000, h = 4000