Calculate the width and length of the fields to minimise the total amount of fencing used A farmer wishes to build a large rectangular grazing field of dimensions width and length, splitting the...
Calculate the width and length of the fields to minimise the total amount of fencing used
A farmer wishes to build a large rectangular grazing field of dimensions width and length, splitting the area into 5 equal sub-fields by dividing the width into 5 equal pieces. The total area of the field must be 11500 square feet. Find the dimensions of the 5 equal sub-fields so that the least amount of fencing is used.
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Let `A` be the total area of the field, `l` be the length of each sub-field and `w` be the width of each sub-field. Let `F` be the total amount of fencing.
Then,
`A = 5lw` (the length of the field is `l` and the total width is `5w`)
`F = 6l +10w` (only one length of fencing is needed to divide two...
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