Question

2 multiple choice 1 point a golden rectangle is to be constructed such that the longest side is 11 inches long. how long is the other side? (round your answer to the nearest tenth of an inch.) 6.0 inches 6.6 inches 6.4 inches 6.8 inches 6.2 inches

Explanation:

Step1: Recall golden - ratio formula

The ratio of the longer side \(a\) to the shorter side \(b\) of a golden rectangle is the golden ratio \(\varphi=\frac{1 + \sqrt{5}}{2}\approx1.618\). So, \(a=\varphi b\), and we can solve for \(b\) when \(a = 11\) inches. The formula for \(b\) is \(b=\frac{a}{\varphi}\).

Step2: Calculate the length of the shorter side

Substitute \(a = 11\) into the formula \(b=\frac{a}{\varphi}\). Since \(\varphi\approx1.618\), then \(b=\frac{11}{1.618}\approx6.8\) inches.

Answer:

6.8 inches