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 L and W are the length and width of the whole paper sheet and l and w are the length and width of each rectangle of the grid then

W = 9 * w
L = 4 * l

We also know that each rectangle is similar in proportion with the whole sheet. That tells us that one of the following is true:

1) L/W = l/w
or
2) L/W = w/l

It's obvious that 1) is not true because L/W = 4*l/9*w which different than l/w.

Then the only possibility is

L/W = w/l = 4*l/9*w => w = l*2/3

We know that:

W = 15 = 9 *w => 15 = 9 * l * 2/3 => l = 5/2

Finaly, the solution is:

L = 4 * l = 4 * 5/2 = 10

Posted by Florin on 2004-03-23 02:36:39