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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

Respuesta :

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