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the fencing problem
Member rating: No Rating | Words: 1898 | Submitted: Tue Oct 23 2007
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The Fencing Problem A farmer wants to fence a plot of level land and has exactly 1000 meters of fencing. The Farmer wants to have a perimeter of 1000m but is not concerned about the shape of the plot. I am going to investigate the maximum area of a land using different families of shapes. I will investigate all families of shapes and see which one has the maximum area. I will be using rectangles, triangles and polygons. First I will be investigating Quadrilaterals and I will be using rectangles to find the maximum area using different lengths and keeping the perimeter the same. Perimeter= Width+Length+Width+Length = 250+250+250+250 = 1000m Area of Rectangle= Width*Length = 250*250 = 62500m( Width (m) Lengths (m) Perimeter (m) Area (mē) 450 50 1000 22500 400 100 1000 40000 350 150 1000 52500 300 200 1000 60000 250 250 1000 62500 200 300 1000 60000 150 350 1000 52000 100 400 1000 40000 50 450 1000 22500 In my investigation I have found that the maximum area is 62500m( with the lengths 250 and 250. In my search I went down by 50 for the Width and up by 50...
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