Penning for Pony

By

Kiisha Gibbs


Problem:

 

To make a pen for his new pony, Ted will use an existing fence as one side of the pen. If he has ninety-six meters of fencing, what are the dimensions of the largest rectangular pen he can make?

 


My first attack on this problem had me beginning with a GSP file.  Because the new fence is rectangular in shape, we know the existing side will determine the opposite side.

After further thought, I went to Excel and created a spread sheet where I created a list that ran through possible integral measures for the existing side, but making sure that the opposite, w, was the same and that “l” + “l” + “w” were a constant of 96. 

            The task now becomes find the maximum area.  You can click here to see the entire spreadsheet that shows the sorted list.  Below are sample from the spreadsheet.

 

 

 

ExistingSide

w

l

l

perimeterof3

AREA

1

1

47.5

47.5

96

47.5

2

2

47

47

96

94

3

3

46.5

46.5

96

139.5

4

4

46

46

96

184

5

5

45.5

45.5

96

227.5

6

6

45

45

96

270

 

 

45

45

25.5

25.5

96

1147.5

46

46

25

25

96

1150

47

47

24.5

24.5

96

1151.5

48

48

24

24

96

1152

49

49

23.5

23.5

96

1151.5

50

50

23

23

96

1150

51

51

22.5

22.5

96

1147.5

52

52

22

22

96

1144

53

53

21.5

21.5

96

1139.5

 

 

90

90

3

3

96

270

91

91

2.5

2.5

96

227.5

92

92

2

2

96

184

93

93

1.5

1.5

96

139.5

94

94

1

1

96

94

95

95

0.5

0.5

96

47.5

96

96

0

0

96

0

 

The maximum area is 1152 squared meters, where the existing side is 48 m and the lengths of adjacent sides are 24 meters.


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