(related to Problem: The Cardboard Box)

The areas of the top and side multiplied together and divided by the area of the end give the square of the length. Similarly, the product of top and end divided by side gives the square of the breadth; and the product of side and end divided by the top gives the square of the depth. But we only need one of these operations. Let us take the first. Thus, $120 \times 96$ divided by $80$ equals $144,$ the square of $12.$ Therefore the length is $12$ inches, from which we can, of course, at once get the breadth and depth — $10$ in. and $8$ in. respectively.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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