Final answer:
The best location for the center of the fountain to be equidistant from the sides of the courtyard involves using geometric constructions, such as perpendicular bisectors, to find the point of intersection which is equidistant from each corner or side of the courtyard.
Step-by-step explanation:
The question is related to finding the center of the fountain such that it is equidistant from the sides of the courtyard, implying a need for the application of geometry. The central point would essentially be the centroid if the courtyard's shape is triangular or the center of the inscribed circle if the courtyard is of any polygonal form where all sides are equidistant from the center.
To find this equidistant point, one would construct the perpendicular bisectors of at least two of the sides of the courtyard. The point where they intersect would be the same distance from each vertex, thereby being the optimal location for the fountain.
If the courtyard is triangular, the construction of angle bisectors or medians would also lead to the center point. If additional shape information is provided, such as a rectangular or circular courtyard, different methods would be used, such as finding the intersection of the diagonals or the radius length from the circle's center to any point on its circumference.