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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Expert Answers
calendarEducator since 2012
write511 answers
starTop subjects are Math, Science, and Business
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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calendarEducator since 2012
write1,275 answers
starTop subjects are Math and Science
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=...
(The entire section contains 2 answers and 323 words.)
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