Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area and then divideit into four pens with fencing parallel to one side of therectangle. What is the largest possible total area of the fourpens?(a) Draw several diagrams illustrating the situation, somewith shallow, wide pens and some with deep, narrowpens. Find the total areas of these configurations. Doesit appear that there is a maximum area? If so, estimate it (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.
Consider the following problem: A farmer with 750 ft of
fencing wants to enclose a rectangular area and then divide
it into four pens with fencing parallel to one side of the
rectangle. What is the largest 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 that there is a maximum area? If so, estimate it
(b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.
Given:
The length of the fencing is 750 ft.
Let the length of two parallel sides of rectangle be x ft and the length of other two parallel sides of rectangle be y ft.
The rectangular area is divided into 4 pens with fencing parallel to one side of rectangle.
Different illustrations of the situation can be
Suppose the 4 pens are parallel to the side with length x ft.
So there will be 5 sides of length x ft and 2 sides of length y ft.
So we can write,
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