# Given a specific number of rectangles, determine their size for them to fit in another larger rectangle

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.
• Also the idea is to maximise the size of the smaller rectangles. – Jeff May 12 at 1:45