SOLUTION: One principle used by the ancient Greeks to get shapes that are pleasing to the eye in art and architecture was the Golden Rectangle. If a square is removed from one end of a Go

Question 204167: One principle used by the ancient
Greeks to get shapes that are pleasing to the eye in art
and architecture was the Golden Rectangle. If a square
is removed from one end of a Golden Rectangle, as shown
in the figure, the sides of the remaining rectangle are
proportional to the original rectangle. So the length
and width of the original rectangle satisfy
L/W = W/L-W
An artist wants her painting to be in the
shape of a golden rectangle. If the length of the painting is
36 inches, then what should be the width?
So far the only thing I have is 36/w = w/36-w. I can't find an example in my book that looks like this equation. I am missing a step somewhere.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
36/w = w/36-w
----
Cross-multiply to get:
36(36-w) = w^2
---
36^2 - 36w = w^2
---
w^2 + 36w - 36^2 = 0
I graphed it and found that w = 22.249..
============================================
Cheers,
Stan H.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
nothing missing ___ you just need to solve the equation

"cross" multiplying ___ 36^2 - 36w = w^2

0 = w^2 + 36w - 1296 ___ use the quadratic formula to find w

*******************ANSWER BELOW*******************************

18 * [sqrt(5) - 1]
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