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 Write-up

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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