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There are infinitely many.

The whole number rectangle are:

1 by 12, 2 by 6 and 3 by 4.

More rectangles have fractional sides, for example starting from the 1 by 12 rectangle:

  • halving the first dimension and doubling the second
0.5 by 24, 0.25 by 48, 0.125 by 96, 0.0625 by 192, ...
  • dividing the first dimension by 5, multiplying the second by 5
0.2 by 60, 0.04 by 300, 0.008 by 1500, 0.0016 by 7500, ...
  • multiplying the first dimension by 5, dividing the second by 5
5 by 2.4, 25 by 0.48, 125 by 0.096, 625 by 0.0192, ...
  • doubling the first dimension, halving the second
(2 by 6, 4 by 3) 8 by 1.5, 16 by 0.75, 32 by 0.375, 64 by 0.1875, ...
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Q: What are all the possible dimesions of a 12 square rectangle?
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