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Question 230837: 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 2ft longer than its width, then for what dimensions would the length and width have the golden rule. I was on this path:
8/5 = x+2/x but that didn't work out.
Can you help please?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! L/W = 8/5 is the golden ratio.
The length of a painting is 2 feet more than the width.
This makes L = W + 2
Golden ratio is L/W = 8/5
If L = W + 2, then the golden ratio becomes (W+2)/W = 8/5
Multiply both sides of this equation by 5 to get:
5 * (W + 2)/W = 8
Multiply both sides of this equation by W to get:
5 * (W + 2) = 8*W
Remove parentheses to get:
5W + 10 = 8W
Subtract 5W from both sides of this equation to get:
3W = 10
Divide both sides of this equation by 3 to get:
W = 10/3
If W = 10/3, then L = W + 2 = 10/3 + 2 = 10/3 + 6/3 = 16/3
L = 16/3
W = 10/3
L/W = (16/3)/(10/3) = (16/3) * (3/10) = 16/10 = 8/5
You have the golden ratio when:
L = 16/3
W = 10/3
L = W + 2 means L = 10/3 + 2 means L = 10/3 + 6/3 means L = 16/3
Both requirements are met.
L = W + 2
L/W = 8/5
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