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.
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
To find the possible lengths of the other side of a golden rectangle given that one side is 3.7 inches, we can use the ratio of the golden ratio, also known as Phi (Φ), which is approximately 1.618.
To determine the shorter length, we divide the given length by Phi:
Shorter length = 3.7 / Φ ≈ 3.7 / 1.618 ≈ 2.287
Rounding this to the nearest tenth, the shorter length can be approximately 2.3 inches.
To determine the longer length, we multiply the given length by Phi:
Longer length = 3.7 * Φ ≈ 3.7 * 1.618 ≈ 5.986
Rounding this to the nearest tenth, the longer length can be approximately 6.0 inches.
Therefore, the possible lengths of the other side of the golden rectangle can be approximately 2.3 inches (shorter length) or 6.0 inches (longer length).