Fencing Problem
Introduction: A farmer has 1000 metres of fencing, and he wants to be
able to get the maximum amount of space that he can with the 1000
metres. By using formulae that we already know, we can find out what
shape can give the most area. I will test each shape to find the
maximum area I can, then I can eventually use the shape that can
create the largest area with 1000 metres of fencing.
First I will look at Rectangles, then all 3 types of triangles,
Pentagons, hexagons and finally circles, and by the end I will have
found out which is the suitable shape to have the fence in.
Rectangle
Width
Length
Area
50
450
22500
100
400
40000
150
350
52500
200
300
60000
250
250
62500
<<
300
200
60000
<<
350
150
52500
Between these three numbers.
400
100
40000
450
50
22500
After finding out the maximum area with a rectangle, I now need to
find the maximum area of a triangle:
Width
Length
Area
200
300
60000
205
295
60475
210
290
60900
I used the heroes formula for these calculations:
215
285
61275
SQRT((500*(500-a)*(500-b)*500-c))
220
280
61600
225
275
61875
230
270
62100
235
265
62275
240
260
62400
245
255
62475
250
250
62500
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