Setting div height based on its width

You can do this with CSS by setting the height to zero and then adding a percentage to padding-bottom. You might have to tweak it a little to get the desired outcome but here's a fiddle with an example http://jsfiddle.net/wbq8o3s7/

#myDiv {
  width: 100%;
  height: 0;
  padding-bottom: 35%;
  background-color: #333;
}

<div id="myDiv"></div>