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 gold

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Question 215506This question is from textbook Elementary & Intermediate Algebra
: 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? This question is from textbook Elementary & Intermediate Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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?
:
Let x = width of the painting
then
(x+2) = length of the painting
:
x%2F%28%28x%2B2%29%29 = 5%2F8
Cross multiply, results
8x = 5(x+2)
:
8x = 5x + 10
:
8x - 5x = 10
:
3x = 10
x = 10%2F3
x = 31%2F3 units wide
and
51%2F3 units long
;
:
Check solution:
5/8 = .625
3.3333/5.3333 = .64998 ~ .625