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February 18th, 2009, 08:08 AM  #1 
Newbie Joined: Feb 2009 Posts: 6 Thanks: 0  Problem of Squares
I've been presented with this problem... " If the smallest square has dimensions 1 x 1, what is the AREA of the rectangle ABCD. This problem is not to be solved using a ruler. " The square then looks like: Where I drew a line out is the smallest square, 1 x 1. Sorry about the bad drawing... In total there's 9 squares within the big square so I guess you could say 10 total? So how does one go about solving this problem? Any solutions would be great. 
February 18th, 2009, 11:16 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,844 Thanks: 1566 
Rotated through ninety degrees, the rectangle is as shown below. The sizes of the component squares are easily found, since they must tally along common edges. The required area is therefore 1056. 
February 18th, 2009, 02:17 PM  #3 
Newbie Joined: Feb 2009 Posts: 6 Thanks: 0  Re: Problem of Squares
Where'd you get these numbers from though? Mind showing me some of the algebra skills you used to solve down... I'd love to see exactly what you did so I know what I'm doing. Thanks a lot man, this is great. 
February 19th, 2009, 12:00 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,844 Thanks: 1566 
The diagram is from this article, which you could have found using a Google search. It explains the method and summarizes some interesting history.


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