Question

a surfer is stranded on an island in the shape of an equilateral triangle. the surfer wants to build a hut where the sum of the distances to the sides of the island is a minimum, because she surfs on each of the three beaches and equal amount of time. Where should she build her hut

Answer 1

The surfer should build her hut at the center of the equilateral triangle. This is because the sum of the distances from the center of an equilateral triangle to its three sides is the minimum possible. This is because the center of an equilateral triangle is the point that is equidistant from all three of its sides. Therefore, if the surfer builds her hut at the center of the island, she will be the same distance from each of the three beaches, and the sum of the distances to the sides of the island will be minimized