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Sally wants to build a rectangular wooden fence with a vertical divider down the middle for use in agriculture. She has $2,016 to spend on fencing and can buy fencing from a local hardware store for $12/foot. What is the maximum area that her fence can enclose under these constraints? Would this change if there were two vertical dividers instead of one? If so, how? Please write your answer in essay format.

User Cmm User
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Answer: 5,292 square feet.

Step-by-step explanation: Since the fence has a vertical divider down the middle, we divide the maximum length in half to determine the length of each side: 168 feet / 2 = 84 feet.

To find the maximum area, we multiply the length of one side by the length of the other side: 84 feet * 84 feet = 7,056 square feet.

Therefore, the maximum area that Sally's fence can enclose under these constraints is 7,056 square feet.

If there were two vertical dividers instead of one, the maximum area that the fence can enclose would change. In this case, Sally would divide the maximum length into four equal sections, as there would be three dividers.

To find the length of each section, we divide the maximum length by four: 168 feet / 4 = 42 feet.

Since there are now four equal sections, we multiply the length of one section by itself and then multiply by three (to account for the three remaining sections): 42 feet * 42 feet * 3 = 5,292 square feet.

Therefore, if there were two vertical dividers instead of one, the maximum area that the fence can enclose would be 5,292 square feet.

Hope this helps!

User Wilhelm
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