Consider the following problem: A farmer with 680 ft of fencing wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. What is
possible total area of the four pens?
(a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear th.
maximum area, A? If so, estimate it. (Round your answer to the nearest thousand.)
A = 11560 ft$^2$
(b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.
y
Let x denote the length of the dividers. Let y denote the length of the perimeter.
• Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides.
Let x denote the length of the perimeter. Let y denote the length of the dividers.
Let y denote the length of each of two sides and three dividers. Let x denote the length of the other two sides.
(c) Write an expression for the total area.
A = $x \cdot y$ ft$^2$
(d) Use the given information to write an equation that relates the variables.
$\frac{680 - 22}{5}$
(e) Use part (d) to write the total area as a function of x.
A = ft$^2$
(f) Finish solving the problem and compare the answer with your estimate in part (a). (Round your answer to the nearest integer.)
A = ft$^2$
