Answer: option a. 5.46
Step-by-step 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
So, since you have thhe given side = 9, you can set the proportion, to find the unknown lenght, s:
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