Final answer:
The designers' intention to place the restrooms equidistant from key park points is a reasonable task in geometry, involving the circumcenter of a triangle, while also considering landscape and park infrastructure for a practical solution.
Step-by-step explanation:
The question assesses the reasonableness of the decision by the designers of a new amusement park to locate the restrooms equidistant from the park's entrance, the fountain, and the food court. This problem can be approached using geometric principles to ensure maximal accessibility and convenience for all park visitors, reflecting a commitment to equity and ease of access within the park's design.
To determine an appropriate location for the restrooms that is the same distance from these three reference points, we could use the concept of a circumcenter of a triangle formed by the entrance, fountain, and food court. The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect and is equidistant from the vertices of the triangle. In real-world applications such as park design, this mathematical solution must also take into consideration the landscape and existing infrastructure to be feasible.