Determine the unknown side length of the golden rectangle with the given side length. s = t=9 a. 5.56 c. 4.94 b. 4.85 d. 5.26 select the best answer from the choices provided

option a. 5.46

Explanation:

The side lengths of the golden rectangle are in the proportion:

          1

golden number

The golden numbrer is:

  1 + √5

     2

So, the ratio is:

       1

   1 + √5
  
       2

And, using the properties of the division of fractions, that is equivalent to:

      2

 1 + √5

Since you have the given side t = 9, you can set the proportion, to find the unknown lenght, s:

    2               s
=  
1 + √5           t

    2               s
=  
1 + √5           9

And you can solve for s:

s = 9 * 2 / (1 + √5) ≈ 18 / (1 + 2.236) = 18 / (3.236) ≈ 5.56.

Which is the option a. 5.56