Fixed ratio element

index.html

<div class="outer">
  <div class="middle">
    <div class="inner">
      Hello world
    </div>
  </div>
</div>

style.css

.outer {
  /* Set this to whatever width you would like */
  width: 85.60mm;
}

.middle {
  /* Set this to the ratio of height:width */
  padding-top: 63.0607476635514%; /* = 53.98mm / 85.60mm */
  position: relative;
}

.inner {
  border: 1px solid gold;
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  right: 0;
}