Golden Rectangle- Fibonacci

Question

A golden rectangle has a longer side of length 180 ft. Which of the following numbers most closely represents the length of the shorter side of the rectangle?

 

a. 291.24 ft

b. 111.25 ft

c. 161.8 ft

d. 100 ft

e. none of these

Answer 1

The Golden Ratio is (1 + √5)/2 ≈ 1.618

 

In a Golden Rectangle, length/width = Golden Ratio

 

So, we want length/width = 1.618

 

180/width = 1.618

 

width = 180/1.618 ≈ 111.25    ANSWER (B)

Answer 2

The shortest side will be less than 180 ft.  The side that is less than 180 ft but close to that value is

 

(c) 161.8 ft