Scale div with fixed aspect ratio (height given)

Question

I'm looking for a way to keep the aspect ratio of a div fixed. I already found posts like this:

• Responsively change div size keeping aspect ratio
• Maintain the aspect ratio of a div with CSS

But these posts always expect the width to be given. I would like to specify a fixed ratio and then specify either height or width.

Examples:

<div class=fixed_ratio style="width: 50px;"></div>
<div class=fixed_ratio style="height: 50px;"></div>

Let's say the fixed_ratio-class uses a fixed ratio of 1:5. The two lines above should result in two div's (50px/250px, 10px/50px).

Is this even possible without javascript?