Dividing a Square into 7 Similar Rectangles

This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectangles have?

This is a companion discussion topic for the original entry at https://johncarlosbaez.wordpress.com/2023/03/06/dividing-a-square-into-7-similar-rectangles/