SOLUTION: James has 500 feet of fencing to enclose a rectangular region on his farm for some sheep. A) Make a sketch of 3 possible regions that James could enclose and give the corresponding

Question 733079: James has 500 feet of fencing to enclose a rectangular region on his farm for some sheep. A) Make a sketch of 3 possible regions that James could enclose and give the corresponding areas. B) If the length of the region is x, find an expression for the width. C) Use your answer from part B to write an equation for the area to the region. D) Graph your equation from part C on your calculator(My teacher never told us to use one of those types of calculators) and sketch the graph. E) James wants his fenced region to have the largest area possible using 500 feet of fencing. Find this area using the graph or a table of values. F) What is the length and width of the region with the area from part E? Describe this region.
What am I supposed to do for parts B, D, E, and how to I describe the region. I really need help on this, and I don't have much time. Please!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
James has 500 feet of fencing to enclose a rectangular region on his farm for some sheep. A) Make a sketch of 3 possible regions that James could enclose and give the corresponding areas.
Comment: The confusion comes from trying to relate part A to B,C,D etc.
I'm going to assume the "region" enclosed by the 500 ft of fencing.
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B) If the length of the region is x, find an expression for the width.
Perimeter = 2(Length + Width)
500 = 2(x + width)
250 = x + sidth
width = 250-x

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C) Use your answer from part B to write an equation for the area to the region.
Area = length*width = x(250-x) = 250x - x^2 sq. ft.
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D) Graph your equation from part C on your calculator(My teacher never told us to use one of those types of calculators) and sketch the graph.

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E) James wants his fenced region to have the largest area possible using 500 feet of fencing. Find this area using the graph or a table of values.
Use what ever method you know to find the "x" value that gives you
the maximum area where A(x) = x(250-x)
Ans: x = 125 ft.

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F) What is the length and width of the region with the area from part E? Describe this region.
Ans: length = width = 125 ft.
The rectangle is a square.
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Cheers,
Stan H.
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