I am trying to find a formula for the height (or width) of the smaller rectangles in the following problem along with the number of rows they require: A given number $N$ rectangles (all of which are of the same size) must fit into another larger rectangle. The smaller rectangles must be in rows that are as even as possible.

Known constants:

  • $N$ - number of smaller rectangles;
  • $R$ - width to height ratio of the smaller rectangles,
  • $R$ is always less than $1$ i.e. width is always less than height;
  • $H$ - height of the larger rectangle;
  • $W$ - width of the larger rectangle,
  • $W$ is always more than H.

Required unknown variables:

  • $w$ - width of the smaller rectangles;
  • $r$ - number of rows of the smaller rectangles with the smaller rectangles being distributed as evenly as possible between the rows.
  • $\begingroup$ Also the idea is to maximise the size of the smaller rectangles. $\endgroup$ – Jeff May 12 at 1:45

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