The side lengths of the golden rectangle are in the proportion ⇒ 1 : golden number
golden number = [tex]\frac{1+\sqrt{5} }{2}[/tex]
So, the ratio = 1 : [tex]\frac{1+\sqrt{5} }{2}[/tex] = [tex]\frac{1}{\frac{1+\sqrt{5} }{2}} = \frac{2}{1+\sqrt{5}}[/tex]
Since we have given side l = 9, we can use the proportion, to find the unknown lenght s.
∴ [tex]\frac{2}{1+\sqrt{5}} = \frac{s}{l}[/tex]
∴ [tex]\frac{2}{1+\sqrt{5}} = \frac{s}{9}[/tex]
Solve for s.
∴ s = [tex]9 * \frac{2}{1+\sqrt{5}} = \frac{18}{1+\sqrt{5}}[/tex]
using the calculator
∴ s ≈ 5.56
So, the correct answer is option a. 5.56
