Answer :
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.