Maintaining aspect ratio on a div with dynamic content

Maintaining aspect ratio on a div with dynamic content

I'm looking for a solution where I have a div that grows dynamically while
maintaining a 1:1 aspect ratio. I've found many solutions with a fixed
width (like this), but they don't work with dynamic content. IE8
compatibility would be a big plus! A JavaScript solution would work too,
but I'd prefer a CSS solution.
Thanks a bunch!