A farmer wishes to build a large rectangular grazing area of dimensions, width (W) and length (L) splitting the area into 5 equal fields by dividing the width into 5 equal pieces. The total area of...

A farmer wishes to build a large rectangular grazing area of dimensions, width (W) and length (L) splitting the area into 5 equal fields by dividing the width into 5 equal pieces. The total area of all the fields must be 10500 square feet. Find the dimensions that use the least amount of fencing.

(It is not always the case that the width is shorter than the length. Round-off your answers to 3 decimal places)

Width W=

Length L=

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mathsworkmusic eNotes educator | Certified Educator

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We have that the perimeter of the field is given by

`P= 6l +2w`

and that the area is given by

`A = lw = 10500`

Notice the symmetry of the problem. The perimeter will be maximised when

`6l = 2w`

`implies` `w = 3l`

Therefore we have that

`A = 3l^2 = 10500`

`implies` `l = sqrt(10500/3) = 59.161` ft

Then `w = 3l = 3(59.16) = 177.482` ft

The length of the field should be 59.161 ft

The total width of the field should be 177.482 ft

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lemjay eNotes educator | Certified Educator

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The formula of area of rectangle is:

`A= Le n g t h* Width`

The given total area of the rectangular grazing lot is 10500 square feet. Its length is represented by L and width by W. So,

`10500=LW`

Solving for W yields:

`W=...

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