The Golden Ratio is the solution of x=1/(1+x) which is the quadratic equation x^2+x-1=0. x=(-1+sqrt(5))/2=0.61803... and -1.61803... Significantly, 1/0.61803... = 1.61803.... So using 1.61803 as the ratio quoted, the length of the rectangle is 8.09cm approx. Therefore a close approximation for the length is 8cm.