ABC is an acute-angled triangle with area 1. A rectangle F(PQRS) has its vertices on the sides of the triangle, with P and Q on BC, R on AC, and S on AB. Another rectangle, G(WXYZ), has its vertices on the sides of triangle ASR, with W and X on RS, Y on AS, and Z on AR.

What is the maximum total area of F and G?

By the same reasoning, with 1, 2, 3, ... n rectangles, the shaded area would be 1/2, 2/3, 3/4, ... (n-1)/n of the total area.

Posted by Federico Kereki on 2004-03-02 14:43:10