Answer
$\frac{2}{1+\sqrt5}$
Work Step by Step
According to the exercise: $\frac{w}{l}=\frac{l}{l+w}$ and $w=1$.
Hence here: $\frac{1}{l}=\frac{l}{l+1}\\l+1=l^2\\l^2-l-1=0$
By the quadratic formula: $l=\frac{1+\sqrt5}{2}$ (the other solution is negative, which is impossible), hence the golden ratio is: $\frac{1}{\frac{1+\sqrt5}{2}}=\frac{2}{1+\sqrt5}$
