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 go

Question 285794: 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?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Golden ratio is 8 to 5.
This is the ratio of the length to the width.
Length of the painting is 2 feet longer than its width.
This means that L = W+2

If the ratio of the length to the width if 8:5, this means that:

L/W = 8/5

Cross multiply to get:

5L = 8W

If L = W+2, you can substitute in this equation to get:

5*(W+2) = 8W

Simplify to get:

5W + 10 = 8W

Subtract 5W from both sides of this equation to get:

10 = 3W

Divide both sides of this equation by 3 to get:

W = 10/3 feet.

When W = 10/3 feet, L = W + 2 = 16/3

With L = 16/3 and W = 10/3, the ratio of L to W is equal to:

(16/3) / (10/3).

Multiply this faction by 3/3 and you get 16/10.

Multiply this fraction by (1/2)/(1/2) and you get:

8/5 which is the golden ratio.

The length and width will have the golden ration when the length = (16/3) and the width = (10/3).

Length of 16/3 is the same as 5.33333333.

Width of 10/3 is the same as 3.33333333.

Length is 2 feet longer than the width because 5.33333333 - 3.33333333 = 2.

ratio of Length to Width if 5.33333333/3.33333333 = 1.6 which is the same as 8/5.

That's your answer:

L = 5.33333333 = (16/3).
W = 3.33333333 = (10/3).

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