Answer:
37.2
Step-by-step explanation:
A golden rectangle is a rectangle that satisfies the following proportion:

Where a is the shortest side and (a+b) is the length of the other side. So, we can replace a by 23 and calculate b as:

Applying cross-multiplication, we get:

Therefore, we can find the solutions to the quadratic function as:
![\begin{gathered} b=\frac{-23\pm\sqrt[]{23^2-(4\cdot1\cdot(-529))}_{}}{2\cdot1} \\ b=14.215 \\ or \\ b=-37.215 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ayst68gxpt0q4kbgz71qkwp9hw6zzs0728.png)
Since -37.215 doesn't have any sense here, the value of b is 14.215
It means that the length of the longest side is:
a + b = 23 + 14.215 = 37.215
So, the answer is 37.2