Question

A manufacturer wishes to make a cereal box in the shape of a golden rectangle, based on the theory that this shape is the most pleasing to the average customer. If the front of the box has an area of 104 in², what should the dimensions be? Round answer to the nearest inch

Answer 1

Let w be the width and l the length of the rectangle. 
Then: $\frac{l}{w}= \frac{1+\sqrt5}{2} \text{ and }lw=104$
Solving the above system we get:
$l= \frac{1+\sqrt5}{2}w\\= \frac{1+\sqrt5}{2}\frac{104}{l}$
Therefore:
$l^2=\frac{1+\sqrt5}{2}104$ then $l=13$,which is the length, 
And then the width $w=\frac{104}{13}=8$