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The Fencing problem.  

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MATHS COURSEWORK: THE FENCING PROBLEM We are told that a farmer has exactly 1000 metres of fencing with which she wishes to fence off a plot of land. The shape of the fence does not concern her; however, what she does wish to do is fence off the plot of land, which contains the maximum area. Therefore, the point of this investigation is to investigate the shape, or shapes of the plot of land that have the maximum area. Starting with rectangles, any 2 different length sides will add up to 500, because each side has an opposite with the same length. Therefore, in a rectangle of 100m X 400m, there are two sides opposite each other that are 100m long and two sides next to them that are opposite each other that are 400m long. This means that you can work out the area if you only have the length of one...

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