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.