Enigma 1715: Open the box
12 September 2012
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From New Scientist #2882, 15th September 2012 [link]
I started with a rectangular piece of card a whole number of centimetres long by a whole number of centimetres wide, one of those numbers being a prime. Then I cut out an identical small square from each corner of the card and discarded the four squares. I folded up the four “flaps” on the remaining piece of card to form an open-topped box, choosing the size of the cut squares so that the volume of this open box was the biggest possible. Having made the box, I found that the length of its rectangular base was four times its width.
What were the dimensions of the original piece of card?