Question

Given one side of a golden rectangle is 3.7 inches, find the possible lengths of the other side. Notice that the other side can be either longer or shorter than 3.7 inches. Round your answers to the nearest tenth and use Greek Phi symbol=1.618.

Answer 1

a/b = b/(a-b)

b^2 = a^2 - ab

a^2 - ab -b^2 = 0

a = [b +/- sqrt(b^2 +4 b^2) ]/2

a = b [ 1 + sqrt 5 ]/2

a = 1.618 b sure enough
now 3.7 could be a or b

if b = 3.7
then a = 5.99 about 6

if a= 3.7
then b = 2.29 about 2.3