Question 95359
Ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio of 8 to 5. 
:
Let x = the width
Then
(x+2) = the length
:
We want to have the golden ratio
{{{8/5}}} = {{{((x+2))/x}}}
:
Cross multiply and you have:
8x = 5(x+2)
8x = 5x + 10
8x - 5x = 10
3x = 10
x = 10/x
x = 3.333 ft is the width
:
Length = 3.333 + 2 = 5.333 ft
:
:
Check our solution, see if it has the golden ratio
{{{5.333/3.333}}} = 1.6 = 8/5