The Fencing Problem

The first 200 words of this essay...

A farmer has 1000m of fencing and wants to fence a plot of land, It can be any shape but must have a perimeter of 1000m investigate the shape to find the maximum possible area using 1000m of fencing

I am going to start investigating different shape rectangles, all which have a perimeter of 1000m. Below are 2 rectangles (not to scale) showing how different shapes with the same perimeter can have different areas.

In a rectangle, any 2 different length sides will add up to 500, because each side has an opposite with the same length. Therefore in a rectangle of 100m X 400m, there are two sides opposite each other that are 100m long and 2 sides next to them that are opposite each other that are 400m long. This means that you can work out the area if you only have the length of one side. To work out the area of a rectangle with a base length of 200m, I subtract 200 from 500, giving 300 and then times 200 by 300.

Below is a table of results i worked out using the above method:

Height

Length

Area