height 50% of width
http://stackoverflow.com/questions/10062811/can-i-set-the-height-of-a-div-based-on-a-percentage-based-width
HTML
<div id="dynamicheight">sdsd</div>
CSS
#dynamicheight {
width: 50%;
background-color: cornflowerblue;
}
JavaScript
$(function() {
var div = $('#dynamicheight');
var width = div.width();
div.css('height', width/2);
});