Fencing Problem
A farmer has exactly 1000 meters of fencing and wants to fence of a
plot of level land. She is not concerned about the shape of the plot
but it must have a perimeter of 1000 m. She wishes to fence of a plot
of land that contains the maximum area. I am going to investigate
which shape is best for this and why.
I am going to start by investigating the different rectangles; all
that have a perimeter of 1000 meters. Below are 2 rectangles (not
drawn to scale) showing how different shapes with the same perimeter
can have different areas.
Text Box: 300Text Box: 50[IMAGE][IMAGE]
Text Box: 450
Text Box: 200
Below is a table of different rectangles.
Height
Length
======
Area
10
490
4900
20
480
9600
30
470
14100
40
460
18400
50
450
22500
60
440
26400
70
430
30100
80
420
33600
90
410
36900
100
400
40000
110
390
42900
120
380
45600
130
370
48100
140
360
50400
150
350
52500
160
340
54400
170
330
56100
180
320
57600
190
310
58900
200
300
60000
210
290
60900
220
280
61600
230
270
62100
240
260
62400
250
250
62500
260
240
62400
270
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, ‘My apples will never get across and eat the cones under his pines, and I tell him. He only says, good fences make good neighbours.’ This shows that there is clearly no substantial reason for the wall to be built but one neighbour carries the view that ‘good neighbours make good fences’ and no
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Rodeo is a sport with long American traditions and loved by many spectators and participants. Past history has shown that rodeo needed to make way for a new era of riders and trainers with a larger emphasis on the welfare of the animals and not be discontinued or banned entirely. Today’s rodeos do not present a danger to the animals because the animals are well-cared for and protected, rodeos have strict rules and the stock are treated as prized animals.
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What she does wish to do is to fence off the plot of land which
Sword and Scabbard, a metalwork of art created in Iran, seventh century A.D. by the Sasanian culture (Sword and Scabbard).
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The Fencing Problem Introduction A farmer has exactly 1000 metres of fencing and wants to use it to fence a plot of level land. The farmer was not interested in any specific shape of fencing but demanded that the understated two criteria must be met: · The perimeter remains fixed at 1000 metres · It must fence the maximum area of land Different shapes of fence with the same perimeter can cover different areas. The difficulty is finding out which shape would cover the maximum area of land using the fencing with a fixed perimeter. Aim The aim of the investigation is to find out which shape or shapes of fencing will cover the maximum area of land using exactly 1000 metres of fencing material. Prediction I am predicting that the maximum area of land covered will be achieved by using the fencing shapes with the greatest number of sides.
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