A farmer with 1000 feet of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? Round to the nearest whole number.

Question

Mathematics

Shaniya Madden

11 July, 18:12

A farmer with 1000 feet of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? Round to the nearest whole number.

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Answers (1)

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Dustin · Answer 1

41,666.67m2

Step-by-step explanation:

Call W the Width and L the Length with 3 pieces.

The total length will be 2W + 3L

The Area is L*W

so,

A = L*W

2W+3L = 1000

Solve for L

3L = 1000-2W

L = (1000-2W) / 3

subtitute for L into the first equation

A = L*W

A = W * (1000-2W) / 3

A = (1000W - 2W^2) / 3

Now, to find the max, set the 1st derivative = 0. I don't know if you know what that means, but ...

dA/dW = 1000/3 - 4W/3 = 0

1000 - 4W = 0

W = 250 meters

Solve for L

2W+3L = 1000

500 + 3L = 1000

3L = 500

L = 166.67 m

Area = 250*500/3 = 41,666.67m2.