Using proportions, the solution for the golden section is given as follows:
|AC|/|AB| = 1.6181.
What is a proportion?
A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, the segment lengths are given as follows:
The following proportion is true for the segment:
|AC|/|AB| = |AB|/|BC|
Hence:
1/x = x/1 - x.
x² = 1 - x
x² + x - 1 = 0.
Which is a quadratic equation with solution x = 0.618.
Then the solution for the golden section is given as follows:
|AC|/|AB| = 1/x = 1/0.618 = 1.6181.
More can be learned about proportions at https://brainly.com/question/24372153
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