SOLUTION: ratio's 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. If the length of a rectangular pa

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: ratio's 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. If the length of a rectangular pa      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 95359: ratio's
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. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and wideth have the golden ratio of 8 to 5.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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. 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 of 8 to 5.
:
Let x = the width
Then
(x+2) = the length
:
We want to have the golden ratio
8%2F5 = %28%28x%2B2%29%29%2Fx
:
Cross multiply and you have:
8x = 5(x+2)
8x = 5x + 10
8x - 5x = 10
3x = 10
x = 10/x
x = 3.333 ft is the width
:
Length = 3.333 + 2 = 5.333 ft
:
:
Check our solution, see if it has the golden ratio
5.333%2F3.333 = 1.6 = 8/5