LADY BELINDA'S GARDEN.
(
Patchwork Puzzles)
Lady Belinda is an enthusiastic gardener. In the illustration she is
depicted in the act of worrying out a pleasant little problem which I
will relate. One of her gardens is oblong in shape, enclosed by a high
holly hedge, and she is turning it into a rosary for the cultivation of
some of her choicest roses. She wants to devote exactly half of the area
of the garden to the flowers, in one large bed, and the other half to be
a path going all round it of equal breadth throughout. Such a garden is
shown in the diagram at the foot of the picture. How is she to mark out
the garden under these simple conditions? She has only a tape, the
length of the garden, to do it with, and, as the holly hedge is so thick
and dense, she must make all her measurements inside. Lady Belinda did
not know the exact dimensions of the garden, and, as it was not
necessary for her to know, I also give no dimensions. It is quite a
simple task no matter what the size or proportions of the garden may be.
Yet how many lady gardeners would know just how to proceed? The tape may
be quite plain--that is, it need not be a graduated measure.
Answer:
All that Lady Belinda need do was this: She should measure from A to B,
fold her tape in four and mark off the point E, which is thus one
quarter of the side. Then, in the same way, mark off the point F,
one-fourth of the side AD Now, if she makes EG equal to AF, and GH equal
to EF, then AH is the required width for the path in order that the bed
shall be exactly half the area of the garden. An exact numerical
measurement can only be obtained when the sum of the squares of the two
sides is a square number. Thus, if the garden measured 12 poles by 5
poles (where the squares of 12 and 5, 144 and 25, sum to 169, the square
of 13), then 12 added to 5, less 13, would equal four, and a quarter of
this, 1 pole, would be the width of the path.
