Question 285794
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).