SOLUTION: The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was approximately 8 to 5, the go

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Question 208674: The golden ratio. The ancient Greeks thought that the
most pleasing shape for a rectangle was one for which the
ratio of the length to the width was approximately 8 to 5,
the golden ratio. 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?
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
Well the rectangular as width w and length w+2. So now we set up a porportion to compare the two ratios and then solve for the width and then we can plug back in and find the length.
so our porportion will be

Now plugging in our expressions we get
%28w%2B2%29%2F%28w%29+=+%288%29%2F%285%29
Now we cross multiply and then solve the resulting equation:
5(w+2) = 8w
5w+10 = 8w
10 = 3w
10/3 feet = w or w = 3.33333333333333333333333 feet
So now we find our length which we know is 2 feet + the width. so l = 10/3 + 2 = 16/3 or 5.333333333333333