document.getElementById("karkas").style.backgroundImage = "url(images/1.png)"

function k(){
   document.getElementById("karkas").style.backgroundImage = "url(images/1.png)"
}

<script>
function k(){
    var length = document.getElementsByName('l')[0].value;
        document.getElementById("karkas").style.width = length+"px";
    var height = document.getElementsByName("h")[0].value;
        document.getElementById("karkas").style.height = height+"px";


   document.getElementById("karkas").style.backgroundImage = "url(images/"+ length +".png)"

    }
</script>
<div id="karkas" style="width:100px;height:200px;background:#ff0000;">hhh</div>
<select name="l" class="measurements" onchange="k()">
    <option value="100" selected="selected">100</option>
    <option value="200">200</option>
</select>

<script>
function k(){
   document.getElementById("karkas").style.backgroundImage = "url('images/fence/one/ЦИФРА.png')"
}
</script>
<div id="karkas" style="width:100px;height:200px;background: url('images/fence/three/1.png');">hhh</div>
<select name="l" class="measurements" onchange="k()">
    <option value="ЦИФРА 1" selected="selected">1</option>
    <option value="ЦИФРА 2">2</option>
</select>

function k(){
   var val= document.getElementsByName('l')[0].value;

   document.getElementById("karkas").style.backgroundImage = "url(images/"+ val +".png)"
}

function k(){
  val = $('[name = l]').val();
  $('#karkas').css('background', 'url(images/'+ val +'.png)');
}