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GCSE Mathematics The Fencing Problem The Problem A farmer has 1000 meters of fencing and wants to fence off a plot of level land. She is not troubled about the shape of the plot but it must have a perimeter of 1000 m. She needs to fence of a plot of land that contains the maximum area. I am going to investigate which shape will give the biggest area and show my working. To start of I will use the simplest shapes and find the largest possible area of each shape. A simple shape is a shape, which has an easy formula to finding its area. For example a rectangle has the formula of length x width to find its area. Rectangle/Square I am going to start by investigating rectangles, that all have a perimeter of 1000 meters. Below are 2 rectangles showing how different shapes with the same perimeter can have...

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