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Math's Coursework- the fencing problem Introduction In this coursework I have been asked to find out which shape gives the biggest area for a farmer with a fence perimeter of 1000 meters. There are many different shapes I am going to investigate keeping the perimeter the same for all. The first shape I am going to investigate is rectangles. There are many different possible lengths of sides for rectangles all with a 1000meter perimeter so I am going to start with the length being the biggest possible and I will then go up in every 50 meters. To find the area of a rectangle I have multiplied the length by the width. My results are shown below. Rectangles Perimeter(M) Length(M) Width(M) Area(M²) 1000 449 1 499 1000 450 50 22500 1000 400 100 40000 1000 350 150 52500 1000 250.5 249.5 62499.75 1000 250 250 62500 1000 249.5 250.5 62499.75 1000 200 300 60000 1000 150 350 52500 1000 100 400 40000 1000 50 450 22500 1000 1 449 499 The biggest area I found here was 62500 meters. This shape is a regular rectangle, a square. To prove that this is the biggest possible area I can get from rectangle I have drawn a graph...

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