Answer
$-6+6\sqrt 5\approx7.4$ inches
Work Step by Step
Length of the rectangle is 12 in. To find width, first set up a proportion using the golden rectangle length to width ratio from the book:
$\frac{1+\sqrt 5}{2}=\frac{12}{w}$
Solve for w to determine width by cross multiplying. That gets us $w(1 + \sqrt 5)= 24$
Now, divide each side by $1 + \sqrt 5$ to get $w=\frac{24}{1+\sqrt 5}$
Next, multiply by the conjugate like this:
$w=\frac{24}{1+\sqrt 5}\times\frac{1-\sqrt 5}{1-\sqrt 5}=\frac{24-24\sqrt 5}{1-5}$
From there, simplify:
$w=\frac{24-24\sqrt 5}{1-5}=\frac{24-24\sqrt 5}{-4}=-6+6\sqrt 5\approx7.4 $
