Golden Thoughts

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

rectangle with triangle inside

Given that the areas of $A1$, $A2$ and $A3$ in the above diagram are equal, show that $${RX\over XS} = {RY\over YQ} = {{\sqrt{5}+ 1}\over 2}$$ so that the points $X$ and $Y$ divide the sides of the rectangle in the golden ratio.



Published June 1999,November 2008,December 2008.