(related to Problem: Lady Belinda's Garden)

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.


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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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