Question

26 multiple choice 2 points if a golden rectangle has a width of 15 feet, what is its length? (round your answer to the nearest tenth of a foot)

Explanation:

Step1: Recall the golden ratio formula

The golden ratio $\varphi=\frac{1 + \sqrt{5}}{2}\approx1.618$. For a golden rectangle, if the width is $w$ and the length is $l$, then $\frac{l}{w}=\varphi$ (assuming $l>w$).

Step2: Substitute the given width into the formula

Given $w = 15$ feet. Using the formula $l=\varphi\times w$. Substitute $\varphi\approx1.618$ and $w = 15$ into the formula: $l=1.618\times15$.

Step3: Calculate the length

$l=1.618\times15 = 24.27$.

Answer:

$24.3$ feet