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.
Calling a the height of each rectangle and b the width, an equation can be created, (a/b)=(9b/4a) because the length of the big rectangle can't equal the length of a smaller rectangle, or a contradiction (9=4) is reached.
Cross multiplying and square rooting gives 2a=3b. This means the sides of the rectangle are in proportion of 2 to 3. If the width is longer than the length, the length would be 10 inches, and if the width is shorter than the length, the length would be 22.5 inches.
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