Question

If one measurement of a golden rectangle is 8.8 inches, which could be the other measurement?

Answer 1

The golden ratio is:

\( 1 : \dfrac{1 + \sqrt{5}}{2} \)

Answer 2

A golden rectangle has sides in proportion to the golden ratio.

The golden ratio is known to be:
\[\frac{ 1+\sqrt{5} }{ 2 }\approx1.618033\]

In our rectangle we know that one measure is 8.8". This leads to two possible cases:

1. 8.8 is the long measure.
2. 8.8 is the short measure.

Case 1: 8.8 is the short measure.
The other measure is then:
\[8.8*\frac{1+\sqrt{5}}{2} = \frac{8+8\sqrt{5}}{2}\approx14.2386\]

Case 2: 8.8 is the short measure.
The other side is then:
\[8.8*\frac{2}{1+\sqrt{5}} = \frac{17.6}{1+\sqrt{5}}\approx5.4387\]


The two possibilities for the other measurement are: 4.24 and 5.44

Answer 3

^14.24

Answer 4

Ah yes, my mistake. 14.32. Just a typo.

Answer 5

\(1 : \dfrac{1 + \sqrt{5}}{2} \)

is approximately the same as

\(1 : 1.61804}

8.8 * 1.61804 = 14.24
8.8/1.61804 = 5.43