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

I made a CSS approach to this that is sized by the viewport width, but maxes out at 100% of the viewport height. It doesn't require box-sizing:border-box. If a pseudo element cannot be used, the pseudo-code's CSS can be applied to a child. Demo

.container {
  position: relative;
  max-width:100vh;
  max-height:100%;
  margin:0 auto;
  overflow: hidden;
}
.container:before {
  content: "";
  display: block;
  margin-top: 100%;
}
.child {
  position: absolute;
  top: 0;
  left: 0;
}

Support table for viewport units

I wrote about this approach and others in a CSS-Tricks article on scaling responsive animations that you should check out.