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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