## Algebra 1

$\approx 4.9$ inches
In the Golden Rectangle Ratio, length to width: $(1+\sqrt{5}):2$. Length is 8, and let $w$ be the width. We set up the following equation: $\frac{w}{8}=\frac{2}{1+\sqrt{5}}$. $w=\frac{16}{1+\sqrt{5}}$ We now multiply both sides by the conjugate of the denominator.$\frac{16}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}=\frac{16(1-\sqrt{5})}{1-5}=\frac{16(1-\sqrt{5})}{-4}=4(\sqrt{5}-1) \approx 4.9$ inches