Question

14 multiple choice 2 points a golden rectangle is to be constructed such that the longest side is 16 inches long. how long is the other side? (round your answer to the nearest tenth of an inch.)

Explanation:

Step1: Recall the golden ratio formula

The golden ratio \(\varphi=\frac{1 + \sqrt{5}}{2}\approx1.618\). For a golden rectangle, if the longer side is \(a\) and the shorter side is \(b\), then \(\frac{a}{b}=\varphi\) (when \(a>b\)) or \(\frac{b}{a}=\varphi\) (when \(b > a\)). Here, assume \(a = 16\) (longer side), and we want to find \(b\). Using the formula \(b=\frac{a}{\varphi}\).

Step2: Substitute the value of \(\varphi\)

Since \(\varphi=\frac{1+\sqrt{5}}{2}\approx1.618\), and \(a = 16\), then \(b=\frac{16}{1.618}\).

$$b=\frac{16}{1.618}\approx9.9$$

Answer:

\(9.9\) inches