By Peter Good

Published Sunday September 20 2026 (link)

Farmer Giles had a square-shaped field, which he divided into nine paddocks by building four straight fences in symmetrical fashion, as shown in the diagram (not to scale). The fence from the SW corner meets the northern edge of the field a two-digit whole number of feet from the NW corner and a three-digit whole number of feet from the NE corner, these two numbers having no common factors. The area of the central paddock divided by the area of the field was a fraction with a perfect square numerator and a perfect fourth power denominator.

What were the two distances mentioned above?