Scale div to fit background image

Let a transparent image dictate the DIV dimensions.
Inside that div put the same image with CSS opacity: 0

<div id="mainHeaderWrapper">
   <img src="path/to/image.jpg"><!-- I'm invisible! -->
</div>

set that image to

#mainHeaderWrapper {
    background: no-repeat url(path/to/image.jpg) 50% / 100%;
}
#mainHeaderWrapper img {
    vertical-align: top;
    width: 100%; /* max width */
    opacity: 0;  /* make it transparent */
}

That way the height of the DIV will be dictated by the containing invisible image, and having the background-image set to center, full (50% / 100%) it will match that image's proportions.

Need some content inside that DIV?

Due to the containing image, you'll need an extra child element that will be set to position: absolute acting as an overlay element

<div id="mainHeaderWrapper">
   <img src="path/to/image.jpg"><!-- I'm invisible! -->
   <div>Some content...</div>
</div>

#mainHeaderWrapper{
    position: relative;
    background: no-repeat url(path/to/image.jpg) 50% / 100%;
}
#mainHeaderWrapper > img{
    vertical-align: top;
    width: 100%; /* max width */
    opacity: 0;  /* make it transparent */
}
#mainHeaderWrapper > div{
    position: absolute;
    top: 0;
    width: 100%;
    height: 100%;
}

If you know the proportions of the image, use percentage padding to define the height of the container. Set height:0 and set vertical padding to a percentage of the width.

They key to this method is that percentage-based vertical padding is always related to width.

According to the box model (w3.org):

The percentage is calculated with respect to the width of the generated box's containing block, even for 'padding-top' and 'padding-bottom'.

Below, the image is 400px X 200px, so the proportion of height to width is 1:2 and padding-top is set to 50%;

#mainHeaderWrapper {
  width: 100%;
  height: 0;
  padding-top: 50%;
  background-image: url('https://dummyimage.com/400x200/');
  background-size: 100% auto;
  background-repeat: no-repeat;
}

<div id="mainHeaderWrapper"></div>
stuff below the image

In another example, the image is 300px X 100px. The height is ⅓ of the width, so the padding-top is set to 33.33%:

#mainHeaderWrapper {
  width: 100%;
  height: 0;
  padding-top:33.33%;
  background-image: url('https://dummyimage.com/300x100/');
  background-size: 100% auto;
  background-repeat: no-repeat;
}

<div id="mainHeaderWrapper"></div>
stuff below the image

Edit:

As prompted by Paulie_D, other content in the div must be positioned absolutely, demonstrated below. I suggest positioning these elements using percentages, as well.

#mainHeaderWrapper {
  width: 100%;
  height: 0;
  padding-top: 33.33%;
  background-image: url('https://dummyimage.com/300x100/');
  background-size: 100% auto;
  background-repeat: no-repeat;
}

div#inner_content {
  position: absolute;
  top: 0;
  width: 100%;
  margin-top: 10%;
  color: #FFF;
  text-align: center;
  font-size: 20px;
}

<div id="mainHeaderWrapper">
  <div id="inner_content">Hello World</div>
</div>
stuff below the image

This can be done without using a dummy image. I will use dimensions of an image I just worked with for example.

The dimensions of my image are 2880x1410. Simplify the dimensions -> 96/47 (I used this simple ratio calculator http://andrew.hedges.name/experiments/aspect_ratio/). Once you have the simplified ratio, plug the height and width to the equation:

height: calc((100vw * W) / H); So mine would read: height: calc((100vw * 47) / 96);

No need to worry about the contents of the div either (unless they dont fit)