L-Shape Halves
To make an
�L-shape�, 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 L-shape itself
and the corner piece removed with
a single
cut. Read on ...
The Problems :
A
The diagram below shows an L-shaped piece of card. ( The shaded part has
been removed from the original larger rectangle )
|
|
Can you find
a straight cut that divides the L-shape 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 L-shape 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 L-shapes ...
D
If you�ve found a technique for cutting both the L-shapes 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 !
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