19.03.2023 - 23:38

ou have 200 feet of fencing available to construct a rectangular pen with a fence divider down the middle as shown below. What dimensions of the pen enclose the largest total area?

Question:

You have 200 feet of fencing available to construct a rectangular pen with a fence divider down the middle as shown below.

What dimensions of the pen enclose the largest total area?

Answers (1)
  • Lavon
    April 5, 2023 в 08:48
    To maximize the area of the pen, we want to make it as close to a square as possible since a square has the largest area for a given perimeter. Let's call the length of each of the four sections x, then the width of the entire rectangle will be 2x (since there are two sections of length x). The perimeter of this rectangle can be calculated as: Perimeter = length + width + length + width = 2x + 2(2x) = 6x We know that we have 200 feet of fencing, so: 6x = 200 x = 33.33 Now we can find the area of the rectangle: Area = length x width = 2x * x = 2x^2 Plugging in our value for x: Area = 2(33.33)^2 = 2222.16 sq. ft. Therefore, the dimensions of the pen that enclose the largest total area would be 66.66 feet by 33.33 feet.
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