Answer
$\approx$14.2ft
Work Step by Step
The golden ratio is $\frac{1+\sqrt{5}}{2}=\frac{length}{width}$. If the length is 23 ft, we solve for $w$, or the width. We can do this by cross multiplying.
$\frac{1+\sqrt{5}}{2}=\frac{23}{w} w(1+\sqrt{5})=46, w=\frac{46}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}=\frac{46-46\sqrt{5}}{1-5}=\frac{46-46\sqrt{5}}{-4}=\frac{23\sqrt{5}-23}{2} \approx 14.2ft$
