[css] Can I set the height of a div based on a percentage-based width?

This can actually be done with only CSS, but the content inside the div must be absolutely positioned. The key is to use padding as a percentage and the box-sizing: border-box CSS attribute:

_x000D_
_x000D_
div {_x000D_
  border: 1px solid red;_x000D_
  width: 40%;_x000D_
  padding: 40%;_x000D_
  box-sizing: border-box;_x000D_
  position: relative;_x000D_
}_x000D_
p {_x000D_
  position: absolute;_x000D_
  top: 0;_x000D_
  left: 0;_x000D_
}
_x000D_
<div>_x000D_
  <p>Some unnecessary content.</p>_x000D_
</div>
_x000D_
_x000D_
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Adjust percentages to your liking. Here is a JSFiddle