I have a sheet of paper with a grid drawn on it, filling the whole paper. This grid has 4 rows and 9 columns, forming 36 congruent rectangles. Also, each of these rectangles is similar in proportion to the whole sheet.

If the sheet is 15 inches wide, how long is it?

If the long side of the rectangles was aligned with the long side of the page, we'd have an impossibility; the small rectangles couldn't be similar to a 4x9 version of itself.

If we align the short side of the rectangles with the long side of the page, we get a solution: the small rectangles are proportional to 2x3, and the paper to 12x18 (12=3x4, 18=2x9).

If the paper width is 15", the length is 22.5".