Finding Image width and height by given maximum width and height with aspectratio

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I am trying to find the image aspectratio,so width/height gives the aspect ratio of any image. But i want to set the image width and height like mozilla sets width and height of an image when i set max-width or max-height to somevalue.

How to do this calculation to find width and height of an image with correct aspect ratio?

new_width = width/height*user_definedwidth;

like this, but i want to calculate both width and height for any image?

How mozilla sets both width and height with aspect ratio when max-width or max-height have set.

I need to show any user uploaded image with correct aspect ratio but large size images need to be resized.

<img src="http://hdcomputerwallpaper.com/wp-content/uploads/2013/12/Puppy-images.jpg" style='max-width:200px;'/>

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