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The Fencing problem A farmer has exactly 1000 metres of fencing to fence of a piece of land. She wishes to fence off a plot of land, which contains the maximum area. I will investigate which shape will provide the maximum amount of area, whilst still maintaining a perimeter of 1000m. I shall start by looking at the shape with the least number of sides, the triangle The equilateral triangle The equilateral triangle is a set of special triangles in which all of the sides have are the same length, and the angles are equal. The isosceles triangle These, as well as the aforementioned equilateral triangle are the only triangles I shall be investigating. This is due to scalene and other irregular triangles have more than one variable, and so it is very difficult to calculate the area for them, as there are infinite combinations. With the isosceles triangle, if I know the base length, then...

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