Using Dissections to Cut and Reshape RectanglesDate: 08/28/2004 at 08:31:15 From: Marcia Subject: Mathematical Excursions Cut a 20x15 piece of paper into two pieces to form a 25x12 piece. I have tried and tried and tried and my parents have tried also but we can't figure it out. This may be a trick question but I can't decide what the trick is. Can you help? Date: 08/30/2004 at 18:40:48 From: Doctor Douglas Subject: Re: Mathematical Excursions Hi Marcia. The trick is to use a stairstep-shape. Here's an example of a 20 x 12 rectangle rearranged into a 15 x 16 rectangle. 20 15 +----+----+----+----+ +----+----+----+ | | | | | + +----+ + + +----+ | | | 12 | | | + +----+ + + +----+ + 16 | | | | | | +----+----+----+----+ +----+ + | | +----+----+----+ Can you figure out how to adapt this for your problem? These types of problems are known as "dissections", and you can read more about them here: Dissection http://mathworld.wolfram.com/Dissection.html - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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