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March 30, 2017

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A farmer has $2400 to spend to fence two rectangular pastures.The local contractor will build the fence at a cost of $6.25/m. What is the largest area that the farmer can have fenced for that price?

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    The farmer can buy $2400 / $6.25/m = 384m of fence. 384m/2 = 192m for each of the 2 rectangular pastures. A square is the rectangle with the largest area for a given perimeter, so each square will have sides of 192m/4 = 48m. Each pasture will thus have area of 48m x 48m = 2304 sq.m, and so the total area for both pastures will be 2304 x 2 = 4608 sq. m.

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