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The Problem A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is concerned about the shape of the plot, but must have a perimeter of 1000m. So it could be 400m 50m 450m 1000m Or anything else with a perimeter (or circumference) of 100m. She wishes to fence of the plot, which contains the maximum area. Investigate the shape, or shapes that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. I am going to investigate different with shapes with the perimeter of 1000 m to find out the maximum area. I will start with rectangles as they have drawn some rectangles already. Then I will try Isosceles triangle and equilateral triangle. Then I will do some regular polygons. The I will try a circle. Rectangle and Square Length Width Area 0 500 0 10 490 4900 20 480 9600 30 470 14100 40 460 18400 50 450 22500 60 440 26400 70 430 30100 80 420 33600 90 410 36900 100 400 40000 110 390 42900 120 380 45600 130 370 48100 140 360 50400 150 350 52500 160 340 54400 170 330 56100 180 320 57600 190 310 58900 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 500 0 0 I have drawn a table of different lengths and...

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