Try setting an aspect ratio AND the handles property:
$( "#resizable" ).resizable({
aspectRatio: 16 / 9,
handles: e
});
The above will create a container that will automatically re-size to a 16/9 aspect ratio, only with a handle on the east side of the container.
Here is the description from the documentation site at http://jqueryui.com/demos/resizable/#option-containment:
If specified as a string, should be a comma-split list of any of the following: n, e, s, w, ne, se, sw, nw, all . The necessary handles will be auto-generated by the plugin.
If specified as an object, the following keys are supported: { n, e, s, w, ne, se, sw, nw }. The value of any specified should be a jQuery selector matching the child element of the resizable to use as that handle. If the handle is not a child of the resizable, you can pass in the DOMElement or a valid jQuery object directly.
Code examples
Initialize a resizable with the handles option specified.
$( ".selector" ).resizable({ handles: n, e, s, w });
Get or set the handles option, after init.
//getter
var handles = $( ".selector" ).resizable( "option", "handles" );
//setter
$( ".selector" ).resizable( "option", "handles", n, e, s, w );