Math Coursework - The Fencing Problem :: Math Coursework Mathematics

The Fencing Problem Aim - to investigate which geometrical enclosed shape would give the largest area when given a set perimeter. In the following shapes I will use a perimeter of 1000m. I will start with the simplest polygon, a triangle. Since in a triangle there are 3 variables i.e. three sides which can be different. There is no way in linking all three together, by this I mean if one side is 200m then the other sides can be a range of things. I am going to fix a dwelling and then draw numerous triangles off this base. I can tell that all the triangles will have the same perimeter because using a setsquare and deuce points can draw the same shape. If the setsquare had to touch these two points and a point was drawn at the 90 angle then a circle would be its locus. Since the size of the set square never changes the perimeter must remain the same. IMAGE The area of a triangle depends on two things the height and the base. The base is flash-frozen i n this example so the triangle that has the biggest height, i.e. the middle triangle, will have the biggest area. The middle triangle turns out to be an icosoles triangle. I am going to cerebrate only on icosoles triangles. I have constructed a formula linking all three sides in and icosoles triangle. IMAGE X X X=any number which is great than 250 and less than 500 ======================================================== 1000 - 2X Using Pythagoras theorem I can find and equation linking a side to the area. ====================================================================== (1000 - 2X) + H = X H = X + (X -500) H = height X 500 - X X - (500-X) H Area 251 249 1000 31.6 7874.1 300 200 50000 223.61 44721.0 333.33