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

Answer 1

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