SOLUTION: 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 8 to 5, the golden ratio. If the length of a rec
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Question 125348: 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 8 to 5, the golden ratio. If the length of a rectangular painting is 2 feet longer than its width, then for what dimension would the length and width have the golden ratio?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'm going to presume that you are expected to calculate this using 8 to 5 as an approximation of the golden ratio, even though the actual golden ratio is an irrational number expressed exactly by
Let x be the unknown width, and then x + 2 would be the unknown length. Since the sides must be in the proportion 8:5, we can write:
Cross-multiplying:
giving us the width. The length is two feet more, so the length is
If you are curious, write back and I'll send you the calculations using the correct value for the golden ratio.
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