The Fencing Problem The problem to be solved is that a farmer needs to find the shape that will have the largest area when it has a perimeter of 1000m, so she can fence off a plot of level land. To do this I will have to look at several shapes and investigate a pattern. My prediction is that all the regular shapes will have the largest area. General Information sqrt = square root, A = area, P= perimeter, x^2=x squared, L= Length, W= width x/1/3=x and one third, n=number of sides, PI=â??,r=radius, C= circumference All diagrams not drawn to scale. Investigating different rectangles [IMAGE] All the rectangles must have a perimeter of 1000m. I have to find the rectangle with the largest area. First I will draw a few shapes to show you a pattern. As you can see, the areas of the rectangles get larger as the difference between the length and width get smaller. Now to find the maximum area I will make a spreadsheet in Excel, along with a graph. [IMAGE] [IMAGE] When entering values for the length I could not have entered 0m or 500m because the shape would not be a rectangle then, it would have been a straight line. The areas in the table increase and then decrease. This proves that the areas of the rectangles get larger as the difference between the length and width get smaller. As observed from the spreadsheet and the line graph, the maximum area is 62500m2. This kind of graph is a quadratic graph. It is a quadratic graph because the equation is quadratic. That means there is only one maximum. This is when the width and breadth are 250m. To

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