LShape Halves To make an
‘Lshape’, you generally cut a rectangular piece out of one corner of a
larger rectangle. The problem of cutting this remaining shape into 2 equal
halves is an interesting one, that also solves the problem of how to balance a
piece of card of this shape, either on the edge of a desk or on a pencil point
... This Problem
goes beyond that and asks whether it is possible to divide both the Lshape itself
and the corner piece removed with
a single
cut. Read on ... The Problems : A
The diagram below shows an Lshaped piece of card. ( The shaded part has
been removed from the original larger rectangle )
Can you find
a straight cut that divides the Lshape into
2 halves of equal area ? Are there other ways to do this ? How many ? B There
are clearly lots of ways to cut Area A into equal halves, but can you find a
single (straight) line to cut both
the corner piece and
the Lshape into equal pieces at the same time ? ( Hint : If you divide A
in two, and ( A + B ) in two, you must have divided B in two as well ) C
Now try your hand at these Lshapes ... D
If you’ve found a technique for cutting both the Lshapes and their
missing corners in two with the same single cut, then you can probably see a way
to solve the same problem for these 2 shapes  even though they look so much
harder ! Open the File as a Word Document

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