11. Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of therectangle. What is the largest possible total area of thefour pens?(a) Draw several diagrams illustrating the situation, somewith shallow, wide pens and some with deep, narrowpens. Find the total areas of these configurations. Does itappear 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 yoursymbols.(c) Write an expression for the total area.(d) Use the given information to write an equation thatrelates the variables.(e) Use part (d) to write the total area as a function of onevariable.alaibod(f) Finish solving the problem and compare the answerwith your estimate in part (a).

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Asked Nov 8, 2019
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11. Consider the following problem: A farmer with 750 ft of
fencing wants to enclose a rectangular area and then divide
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11. Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide

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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.
(c) Write an expression for the total area.
(d) Use the given information to write an equation that
relates the variables.
(e) Use part (d) to write the total area as a function of one
variable.
alaibod
(f) Finish solving the problem and compare the answer
with your estimate in part (a).
help_outline

Image Transcriptionclose

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. (c) Write an expression for the total area. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the total area as a function of one variable. alaibod (f) Finish solving the problem and compare the answer with your estimate in part (a).

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Expert Answer

Step 1

 

Given that

Length of fencing is 750 ft

Step 2
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a) Here are three diagrams. The area of the one on the left is 12500 ft2, the area of the middle one is 12500 ft2, and the area of the one on the left is 9000 ft2. It seems that there is a maximum and I would put it at around 13000 ft2 75 125 120 250 100 50

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Step 3
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b) Let x be one side of the overall pen and y the other. The general situation is 'х

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