Calculate nearest possible dimension value PHP (keeping ratio)

I am trying to implement API for image resizing. It is created not exactly for image processing, this is only one part/feature of API.

What I want to implement.

I have url for retrieving image from server it looks like

 http://ift.tt/1FXK0k1

This url will return URL to full image of product with id 42.

Everything is ok.

We can specify desired size with GET parameters like this

 http://ift.tt/1O5vsIO

It also looks fine

But my question if following.

As we can have different images on server with different dimension and aspect ratio, I need to keep this ratio while resizing.

For example I need image to fit 200x300 container but I have 1024x576 (16:9) image on the server. I need to resize this image but keep initial aspect ratio(16:9) but to fit desired container.

How can I efficiently calculate new image size to return depending on incoming desired dimension and current image aspect ratio.

I want to thank everyone in advance for any help or advises.