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 each little rectangle measurements are a x b units, then either:<p>
a/b = 4a/9b   or  <p>
a/b = 4b/9a  <p>

the first way leads to 4ab = 9ab so it has to be the other way <p>
9a^2 = 4b^2 <p>
3a = 2b

There are 2 answers: <p>

Width 15, Height 22.5  (little rectangles 3.75 x 2.5)    or  <p>
Width 15, Height 10     (little rectangles 2.5 x  5/3)

just so the ratio between sides is 2 to 3

and that's my story

Edited on March 22, 2004, 3:13 pm

Posted by Larry on 2004-03-22 15:12:46