Fencing Problem

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Fencing Problem

In this piece of coursework I shall try to obtain the biggest possible area enclosed by 1800m of fencing. I shall look at different types of sizes and shapes of fences to obtain the biggest area.

First I shall look at rectangles as they are easiest to calculate.

P=2L+2w

800=2L+2w

900=L+w

900-w=L

I shall use this formula to work out different lengths by substituting a different number for w.

A=L x w

A=(900-w) x w

w

l=900-w

Area=w(900-w)

50

00

50

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900-50=850

900-100=800

900-150=750

900-200=700

900-250=650

900-300=600

900-350=550

900-400=500

900-450=450

900-500=400

900-550=350

900-600=300

900-650=250

900-700=200

900-750=150

900-800=100

900-850=50

50(900-50)=42500

00(900-100)=80000

50(900-150)=112500

200(900-200)=140000

250(900-250)=162500

300(900-300)=180000

350(900-350)=192500

400(900-400)=200000

450(900-450)=202500

500(900-500)=200000

550(900-550)=192500

600(900-600)=180000

650(900-650)=162500

700(900-700)=140000

750(900-750)=112500

800(900-800)=80000

850(900-850)=42500

I tabulated the results because it allows you to see the different areas with the different lengths. This table shows that a rectangle of both lengths and widths of 450 (square) gives the biggest area in terms of the rectangle.

I shall plot my results onto a graph to see the correlation between them.

The line of symmetry shows the biggest area when you have 1800m of fencing in the shape of a rectangle. I found the ideal dimensions were if the length and width of the rectangle were 450m. This gives you the biggest area of 202500cm².
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Now that I have found the largest area in rectangles I shall move on to find the largest area in an isosceles triangle. I shall look at an isosceles triangle simply because they are

easiest to calculate out of all the triangles. I predict the 3 sides which will produce the largest area will be when they are all 600 because everything is equal.

h²=850²-50²

h²=720,000

Vh²=V720,000

h=848.5281374

Area =(bxh)/2

(848.5281374x100/2= 42,426.40687cm².

h²=800²-100²

h²=600,000

Vh²=V600,000

h=744.5966692

Area =(bxh)/2

(744.5966692x200)/2=77,459.66692cm².

Base

Area(V(900(900-base)(900-side 1)(900-side ...

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