G1.1 In Figure $1, A E F D$ is a unit square. The ratio of the length of the rectangle $A B C D$ to its width is equal to the ratio of the length of the rectangle $B C F E$ to its width. If the length of $A B$ is $W$ units, find the value of $W$.
$\begin{array}{l}\frac{W}{1}=\frac{1}{W-1} \\ W^{2}-W-1=0 \Rightarrow W=\frac{1+\sqrt{5}}{2}\end{array}$