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Using Dissections to Cut and Reshape Rectangles

Date: 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/ 
Associated Topics:
High School Geometry
High School Puzzles

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