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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?

- - =


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).

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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