Let x = the length of one side of the rectangular field and let y = the length of the other side. The Area of the enclosed rectangular field is:

Area = x*y = 2,000,000 ft^{2}

Therefore y = 2,000,000/x

The length of the fence enclosing the area is 2x + 2y. Add another x for the fence dividing the area in half. The Length of the fence, then, is:

L = 2x + 2y + x = 3x + 2y

Since y = 2,000,000/x

L = 3x + 2(2,000,000/x) = 2x + (4,000,000/x)

To find the minimum length, take the derivative of L, set it to zero, and solve for x:

dL/dx = 2 - (4,000,000/x^{2})

0 = 2 - (4,000,000/x^{2})

2,000,000 = x^{2}

**10**^{3}√2 ≅ 1414.2 ft = x [-1414.2 is also a solution, but we can't have a negative length of fence]

**y =** 2,000,000/x = 2*10^{6}/10^{3}√2 = **
10**^{3}√2 ≅ 1414.2 ft [the enclosed area is a square]

**L =** 3x + 2y = 5(10^{3}√2) =
**5000√2 ≅** **7071.1 ft**

**CHECK**:

Area = (10^{3}√2)*(10^{3}√2) = 2*10^{6} = 2,000,000 ft^{2}

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