In order to find the optimum pen, or the pen with the greatest area, I knew
that I needed to organize all the possible rectangles using 48 meters. I started
with the obvious one, 1 by 23, and drew it on quarter inch graph paper. Then
I worked up by decreasing the length by one and increasing the width by one
each time. I continued this way until I was sure that I had all of the possible
rectangles. I knew this because I had used all of the numbers up to 23. I couldnt
use 24 because there would be no width.
The optimum pen was exactly a square. On Pens One the optimum pen was also a square. I think that the reason for this is that in a square there are more square centimeters that dont use any fencing.
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