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Lying and Cheating

Age 11 to 14 Challenge Level:

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it! Clearly there is something wrong here but can you explain what it is?

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Take some squared paper and cut out a rectangle 10 units by 11 units. As shown in the diagram, cut along the diagonal and cut off the two red triangles, each of which has a side of length one unit. Put the two red triangles to one side.

Now slide the right hand piece down (moving one edge that had been the diagonal along the other) until you make another rectangle. The top edge of the new rectangle is 10 units long but the left hand edge becomes 11 units. Thus the new rectangle is the same as the one you started with. (11 units by 10 units).