A new wildlife park has the shape of a square of side 100 km.
The park authorities want to divide the park into three regions, in each of which a ranger station will be built to have oversight of all the points in that region. The regions are to be of equals area, and the ranger stations located so the greatest distance separating any station from a point in its domain is as small as possible.
One idea is to divide the park into three equal strips as shown below, which obviously produces regions of equal area, satisfying the first requirement.
In this arrangement the furthest distance from a station to a point in its region is equal to the length of the dotted line, about 52.7 km. Can you find an alternative way to divide up the park so the furthest distance is less than this?
The Three Ranger Stations
A new wildlife park has the shape of a square of side 100 km.
The park authorities want to divide the park into three regions, in each of which a ranger station will be built to have oversight of all the points in that region. The regions are to be of equals area, and the ranger stations located so the greatest distance separating any station from a point in its domain is as small as possible.
One idea is to divide the park into three equal strips as shown below, which obviously produces regions of equal area, satisfying the first requirement.
In this arrangement the furthest distance from a station to a point in its region is equal to the length of the dotted line, about 52.7 km. Can you find an alternative way to divide up the park so the furthest distance is less than this?