I guess you are converting the image via MediaItem.GetMediaStream(), building a byte array of it and after that you are building a base64 string out of the image. The problem of resizing now becomes a .net problem rather than Sitecore`s. There are several ways to resize image in c#. You can refer to this post s on stack overflow on how to resize the image:
How I can resize the image in c#?
Resize image on the fly in .net and c#
If you decide to drop the code part for resizing and use the Sitecore MediaManager instead there are query string params which will help you resize the image itself. You can refer to this blog post for more information about the query string parameters.