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Title
Penning for Pony 

Problem Statement
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?.

Problem setup

Restated, this problem asks us to find the length and width of the pen, given that the perimeter is 96 meters.

 

Plans to Solve/Investigate the Problem

My initial plan to solve this problem was to “guess-timate.”  I planned on starting at the lowest possible perimeter for the pen, which is 1 meter by 94 meters, and continuing to increase my length by one to determine the width and area. 

 

Investigation/Exploration of the Problem

 I created a spreadsheet which gave me the length, width, and area of the 3 sided fence.

length

length

width

area

1

1

94

94

2

2

92

184

3

3

90

270

4

4

88

352

5

5

86

430

6

6

84

504

7

7

82

574

8

8

80

640

9

9

78

702

10

10

76

760

11

11

74

814

12

12

72

864

13

13

70

910

14

14

68

952

15

15

66

990

16

16

64

1024

17

17

62

1054

18

18

60

1080

19

19

58

1102

20

20

56

1120

21

21

54

1134

22

22

52

1144

23

23

50

1150

24

24

48

1152

25

25

46

1150

26

26

44

1144

27

27

42

1134

28

28

40

1120

29

29

38

1102

30

30

36

1080

31

31

34

1054

32

32

32

1024

33

33

30

990

34

34

28

952

35

35

26

910

36

36

24

864

37

37

22

814

38

38

20

760

39

39

18

702

40

40

16

640

41

41

14

574

42

42

12

504

43

43

10

430

44

44

8

352

45

45

6

270

46

46

4

184

47

47

2

94

48

48

0

0

The section highlighted in yellow is the largest area created with the dimensions given.  As you can see, after the highlighted portion, the numbers begin to decrease. 

 

Extensions of the Problem

There was an extension included with this problem:

Ted actually has another 3/4 of a foot for fencing.  How does this change the dimensions of the pen?

We did not complete it in class.  However, we did create a quadratic equation for the information above:  96x-2x^2.    

Author & Contact
Mesha Rainey
mrainey@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
Area of a polygon

 

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