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2 years ago

A farmer has 1800 m of fencing. He needs to create

Mathematics

1 answer:

NeTakaya2 years ago

7 0

Answer:

67,500 m²

Step-by-step explanation:

ASSUMING the fields look like this __________________

| | |

| | | W

|_________|_________|

Let L be the length of the combined field and W be the width

2L + 3W = 1800

2L = 1800 - 3W

L = 900 - 1.5W

A = LW

A = (900 - 1.5W)W

A = 900W - 1.5W²

Area will be maximized when the derivative equals zero.

dA/dW = 900 - 3W

0 = 900 - 3W

3W = 900

W = 300 m

L = 900 - 1.5(300)

L = 450 m

A = LW = 450(300) = 135,000 m²

so each sub field is 135000/2 = 67,500 m²

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