You can solve that using display table.
Here is the updated JSFiddle that solves your problem.
CSS
.body {
display: table;
background-color: green;
}
.left-side {
background-color: blue;
float: none;
display: table-cell;
border: 1px solid;
}
.right-side {
background-color: red;
float: none;
display: table-cell;
border: 1px solid;
}
HTML
<div class="row body">
<div class="col-xs-9 left-side">
<p>sdfsdf</p>
<p>sdfsdf</p>
<p>sdfsdf</p>
<p>sdfsdf</p>
<p>sdfsdf</p>
<p>sdfsdf</p>
</div>
<div class="col-xs-3 right-side">
asdfdf
</div>
</div>