Question 230837
L/W = 8/5 is the golden ratio.


The length of a painting is 2 feet more than the width.


This makes L = W + 2


Golden ratio is L/W = 8/5


If L = W + 2, then the golden ratio becomes (W+2)/W = 8/5


Multiply both sides of this equation by 5 to get:


5 * (W + 2)/W = 8


Multiply both sides of this equation by W to get:


5 * (W + 2) = 8*W


Remove parentheses to get:


5W + 10 = 8W


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


3W = 10


Divide both sides of this equation by 3 to get:


W = 10/3


If W = 10/3, then L = W + 2 = 10/3 + 2 = 10/3 + 6/3 = 16/3


L = 16/3
W = 10/3


L/W = (16/3)/(10/3) = (16/3) * (3/10) = 16/10 = 8/5


You have the golden ratio when:


L = 16/3
W = 10/3


L = W + 2 means L = 10/3 + 2 means L = 10/3 + 6/3 means L = 16/3


Both requirements are met.


L = W + 2
L/W = 8/5