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:
`(l)/(w)= (1+\sqrt5)/(2) \text{ and }lw=104`
Solving the above system we get:

`l= (1+\sqrt5)/(2)w\\= (1+\sqrt5)/(2)(104)/(l)`
Therefore:

`l^2=(1+\sqrt5)/(2)104` then
`l=13`,which is the length,
And then the width
`w=(104)/(13)=8`