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?A farmer wants to fence in an area of 1.5 million square feet in a rectangular field
Chapter 4, Problem 13(choose chapter or problem)
A farmer wants to fence in 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?
Questions & Answers
QUESTION:
A farmer wants to fence in 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?
ANSWER:Step 1 of 5
Farmer wants to fence an area of 1.5 million square feet in a rectangular field. Let the length of the rectangular field be x and width be y. He divides the rectangle in half with a fence parallel to one of the sides of the rectangle.
Area of the plot will be \(A=x y\)
Given
\(\begin{array}{l}A=1.5 \text{ million square feet}\\
=1.5 \times 10^{6} \text{ square feet}\end{array}\)
So,
\(\begin{array}{l}
x y=1.5 \times 10^{6} \\
y=\frac{1.5 \times 10^{6}}{x}
\end{array}\)