How can I set image size relative to parent height in CSS?

If your height is bigger and width is smaller than container, width will be stretch to 100% and height will be trimmed from both side. Same goes for larger width as well.

Your need, HTML:

<div class="img-wrap">
  <img src="http://lorempixel.com/300/160/nature/" />
</div>
<div class="img-wrap">
  <img src="http://lorempixel.com/300/200/nature/" />
</div>
<div class="img-wrap">
  <img src="http://lorempixel.com/200/300/nature/" />
</div>

And CSS:

.img-wrap {
  width: 200px;
  height: 150px;
  position: relative;
  display: inline-block;
  overflow: hidden;
  margin: 0;
}


div > img {
  display: block;
  position: absolute;
  top: 50%;
  left: 50%;
  min-height: 100%;
  min-width: 100%;
  transform: translate(-50%, -50%);
}