The Fencing Problem

... Maths coursework THE FENCING PROBLEM Investigation A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter (or circumference) of 1000m. She wishes to fence off the plot of land, which contains the maximum area. Therefore, my aim is to investigate the shape, or shapes that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. Rectangles I will start with working out the area of rectangles as it is easy to find its area. 22,500m2 40,000m2 52,500m2 60,000m2 62,500m2 60,000m2 52,500m2 40,000m2 22,500m2 Table Width / m Height / m Area / m2 50 450 22,500 100 400 40,000 150 350 52,500 200 300 60,000 250 250 62,500 300 200 60,000 350 150 52,500 400 100 40,000 450 50 22,500 Graph The table shows that the maximum area of a rectangle with a perimeter of 1000m is a 250 x 250 square. Proof In the graph, if we look at one point on either side of the highest point, they are clearly

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