<div class="container">
    <div class="column">Stretch to fill?</div>
    <div class="column">
        <select size="15">
            <option>Option 1</option>
            <option>Option 2</option>
        </select>
    </div>
<div>

.container {
    padding: 5px;
    border: 1px solid black;
}

.container .column {
    display: inline-block;
    width: 40%;
    background-color: #AAA;
    padding: 5px;
    margin: 5px;
    vertical-align: top;

    height: 100%;
}

select {
    width: 100%;
}

.cf:before,
.cf:after {
    content: " "; /* 1 */
    display: table; /* 2 */
}

.cf:after {
    clear: both;
}


*, *:before, *:after {
  -moz-box-sizing: border-box; -webkit-box-sizing: border-box; box-sizing: border-box;
 }

.faux-columns {
  width: 80%;
  margin:3em auto;
background-image: -webkit-linear-gradient(left, #f2f7fa 25%, #fff 75%);
background-image: -moz-linear-gradient(left, #f2f7fa 25%, #fff 75%);
background-image: -o-linear-gradient(left, #f2f7fa 25%, #fff 75%);
background-image: linear-gradient(left, #f2f7fa 25%, #fff 75%);
background: -webkit-gradient(linear, left top, right top, color-stop(0%,#f2f7fa), color-stop(25%, #f2f7fa), color-stop(25%,#ffffff), color-stop(100%,#ffffff));
background: -moz-linear-gradient(left, #f2f7fa 0%, #f2f7fa 25%, #ffffff 25%, #ffffff 100%);
background: -webkit-gradient(linear, left top, right top, color-stop(0%,#f2f7fa), color-stop(25%,#f2f7fa), color-stop(25%,#ffffff), color-stop(100%,#ffffff));
background: -o-linear-gradient(left, #f2f7fa 0%,#f2f7fa 25%,#ffffff 25%,#ffffff 100%);
background: -ms-linear-gradient(left, #f2f7fa 0%,#f2f7fa 25%,#ffffff 25%,#ffffff 100%);
background: linear-gradient(left, #f2f7fa 0%,#f2f7fa 25%,#ffffff 25%,#ffffff 100%);
border:1px solid #c1c1c2;
}

.col-1, .col-2 {
  float:left;
  vertical-align:top;
  padding:2em 3em;
 }

.col-1 {
  position:relative;
  width:25%;
  background:#F2F7FC;
  border-right:1px solid #c1c1c2;

}

.col-2 {
  width:75%;
  border-left:1px solid #c1c1c2;
  margin-left: -1px;

}

.col-1:after,
.col-1:before {
   top:100%;
   border:solid transparent;content:"";
   height:0;
   width:0;
   position:absolute;
   pointer-events:none;
   display:block;
}
.col-1:after  {
  border-color: rgba(255, 255, 255, 0) rgba(255, 255, 255, 0) rgba(255, 255, 255, 0) #f2f7fa;
  border-style: solid;
  border-width: 21px 0 21px 22px;
  left:100%;
  top: 47px;
}
.col-1:before {
  border-color: rgba(0, 0, 0, 0) rgba(0, 0, 0, 0) rgba(0, 0, 0, 0) #c1c1c2;
  border-style: solid;
  border-width: 22px 0 22px 23px;
  left: 100%;
  top: 46px; }

<div class="faux-columns cf">
  <div class="col-1">
    <h4>First column with bordered triangle pseudo element attached to it. The background needs to be the full height of .faux-columns</h4>
  </div>
  <div class="col-2">
    <h4> Second column which in some cases will be much taller than column</h4>
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  </div>
</div>