Question

Determine the unknown side length of the golden rectangle with the given side length.

Answer 1

Answer: 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