Mathematics - The Fencing Problem

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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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