Problem 61086. Covering a four-pointed star polygon by rectangles

Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).
Given (A, L), return the 2x2 matrix M, where
  • the first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);
  • the second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).
input: (A, L)
output: M = [y1 y2; z1 z2]
Solve

Solution Stats

85.71% Correct | 14.29% Incorrect
Last Solution submitted on Dec 03, 2025

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