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?

This problem is impossible mathematically.

15 = width of large rectangle
x = height of large rectangle

15/9 = width of small rectangle
x/4 = height of small rectangle

For the large and small rectangles to be similar, the following proportion must hold true:

15 : x = 15/9 : x/4

If you simplify, you get 15/4 = 15/9, which isn't true.

You can have a large rectangle broken up into 36 similar smaller rectangles, but only if it has 6 rows and 6 columns. Then, it wouldn't matter how tall the rectangle is. Any height would work.

Posted by Devon on 2004-03-31 18:00:42