Question

Determine the unknown side length of the golden rectangle with the given side length. s = _____, l=9 a. 5.56 c. 4.94 b. 4.85 d. 5.26

Answer 1

The side lengths of the golden rectangle are in the proportion ⇒ 1 : golden number

golden number = $\frac{1+\sqrt{5} }{2}$

So, the ratio = 1 : $\frac{1+\sqrt{5} }{2}$ = $\frac{1}{\frac{1+\sqrt{5} }{2}} = \frac{2}{1+\sqrt{5}}$

Since we have given side l = 9, we can use the proportion, to find the unknown lenght s.

∴ $\frac{2}{1+\sqrt{5}} = \frac{s}{l}$

∴ $\frac{2}{1+\sqrt{5}} = \frac{s}{9}$

Solve for s.

∴ s = $9 * \frac{2}{1+\sqrt{5}} = \frac{18}{1+\sqrt{5}}$

using the calculator

∴ s ≈ 5.56

So, the correct answer is option a. 5.56