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Fencing Problem - Math's Coursework Fencing Problem - Math's Coursework A farmer has exactly 1000 meters of fencing and wants to fence of a plot of level land. She is not concerned about the shape of the plot but it must have a perimeter of 1000 m. She wishes to fence of a plot of land that contains the maximum area. I am going to investigate which shape is best for this and why. I am going to start by investigating the different rectangles; all that have a perimeter of 1000 meters. Below are 2 rectangles (not drawn to scale) showing how different shapes with the same perimeter can have different areas. http://biketrader@www.virgin-bikes.co.uk/dsp_frameset.cfm?&cfid=2124468&cftoken=63911407 Text Box: 300 Text Box: 50 Text Box: 450 Text Box: 200 Below is a table of different rectangles. Height Length Area 100 400 40000 200 300 60000 210 290 60900 220 280 61600 230 270 62100 240 260 62400 250 250 62500 260 240 62400 270 230 62100 280 220 61600 290 210 60900 300 200 60000 310 190 58900 320 180 57600 330 170 56100 340 160 54400 350 150 52500 360 140 50400 370 130 48100 380 120 45600 390 110 42900 400 100 40000 410 90 36900 420 80 33600 430 70 30100 440 60 26400 450 50 22500 460 40 18400 470 30 14100 480 20 9600 490 10 4900 Using this table I can draw a graph of height against area. This is on the next sheet. As you can see, the graph has formed a...

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