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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

User Apurva
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1 Answer

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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

User Hocho
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