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

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Question 192009This question is from textbook Elementary and intermediate algebra
: The ancient Greeks thought that the most pleasing shape for a rectangle was one for which has 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 and intermediate algebra

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


Golden Ratio: L%2FW=8%2F5

And the painting, L=+W%2B2ft, Length is 2 ft longer than Width.
Substitute this "L" to our Golden Ratio:

highlight%28W%2B2ft%29%2FW=8%2F5

Cross multiply,
%285%29%28W%2B2%29=%288%29%28W%29
5W%2B10=8W
10=8W-5W
10=3W -----> 10%2F3=cross%283%29W%2Fcross%283%29
red%28W=%2810%2F3%29ft%29}Width

So, L=W%2B2=10%2F3%2B2=%2810%2B6%29%2F3
red%28L=%2816%2F3%29ft%29} Length

Let us check on our Golden Ratio:
8%2F5=L%2FW=%2816%2F3%29%2F%2810%2F3%29
8%2F5=%2816%2Fcross%283%29%29%28cross%283%29%2F10%29
8%2F5=16%2F10
Reduce left term by dividing both num.&den. by "2":
8%2F5=cross%2816%298%2Fcross%2810%295
highlight%288%2F5=8%2F5%29


Thank you,
Jojo