Height equal to dynamic width (CSS fluid layout) [duplicate]

[Update: Although I discovered this trick independently, I’ve since learned that Thierry Koblentz beat me to it. You can find his 2009 article on A List Apart. Credit where credit is due.]

I know this is an old question, but I encountered a similar problem that I did solve only with CSS. Here is my blog post that discusses the solution. Included in the post is a live example. Code is reposted below.

#container {
  display: inline-block;
  position: relative;
  width: 50%;
}

#dummy {
  margin-top: 75%;
  /* 4:3 aspect ratio */
}

#element {
  position: absolute;
  top: 0;
  bottom: 0;
  left: 0;
  right: 0;
  background-color: silver/* show me! */
}

<div id="container">
  <div id="dummy"></div>
  <div id="element">
    some text
  </div>
</div>