Question

Determine the unknown side length of the golden rectangle with the given side length. s = _____, l=9 a. 5.56 c. 4.94 b. 4.85 d. 5.26

Answer 1

The side lengths of the golden rectangle are in the proportion ⇒ 1 : golden number

golden number =
`(1+√(5) )/(2)`

So, the ratio = 1 :
`(1+√(5) )/(2)` =
`(1)/((1+√(5) )/(2)) = (2)/(1+√(5))`

Since we have given side l = 9, we can use the proportion, to find the unknown lenght s.

∴
`(2)/(1+√(5)) = (s)/(l)`

∴
`(2)/(1+√(5)) = (s)/(9)`

Solve for s.

∴ s =
`9 * (2)/(1+√(5)) = (18)/(1+√(5))`

using the calculator

∴ s ≈ 5.56

So, the correct answer is option a. 5.56