SOLUTION: The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangel was one for which the ratio of the length to the width was approximately 8 to 5, the golde

Question 206775This question is from textbook Elementary and intermediate algebra
: The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangel 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 rectangle painting is 2 feet longer than its width, then for what dimensions would the length and the width have to the golden ratio? Ok, the ratio is L=8 to W=5. However, the length is 2 feet more, so is the L=8+2 and W=5. Would the golden ratio be 10 to 5? I am lost. This question is from textbook Elementary and intermediate algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The ancient Greeks thought that the most pleasing shape for a rectangel 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 rectangle painting is 2 feet longer than its width, then for what dimensions would the length and the width have to the golden ratio?
Ok, the ratio is L=8 to W=5. However, the length is 2 feet more, so is the L=8+2 and W=5. Would the golden ratio be 10 to 5?
---
Let the width be "x" ft.
Then the length is "x+2" ft
-------------------
Proportion:
(x+2)/x = 8/5
8x = 5(x+2)
8x = 5x + 10
3x = 10
x = 3 1/3 ft (this is the width)
x+2 = 5 1/3 ft (this is the length)
=======================================
Cheers,
Stan H.

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