A farmer wants to fence an area of 1.5 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. How can he do this so as to minimize the cost of the fence?
i know one of my equations is
A=xy=1500000
but other than that i have no idea how to solve it
Considering all possible rectangles with a given area, the square has the smallest perimeter
Proof:
Consider a square of dimensions "x "by "x", the area of which is x^2.
Subtract "a" from one side making it (x - a).
Add "b" to the other side making it (x + b).
Since x^2 - ax + b(x - a) = A, "b" must be greater than "a" as "ax" must equal b(x - a).
Therefore, P = 2(x - a) + 2(x + b) = 2x - 2a + 2x + 2b = 4x - 2a + 2b.
With "b" greater than "a", 4x - 2a + 2b results in a greater perimeter P.
Consider the family of rectangles with area 36 sq.units.
The rectangle dimensions and their associated perimeters are:
x......1......2......3......4......6
y.....36....18....12......9......6
P....74....40....30.....26....24 showing that the square has the smallest perimeter.
What is the perimeter of a square field of 1,500,000 sq.ft. with a dividing fence down the middle?
What is the perimeter of two adjoining squares each of 750,000 sq.ft.