Area of a square and proportions of a rectangle

Hi there, 

I need a help with this one

The problem is as follows:

I begin by creating a square. Its dimension is determined by the square root of the area (first input slider). What I'd like to do next is to scale it non-uniformly so that I can get a rectangle with a specific proportion. This proportion (my second input slider) is always larger than 0 and below 1. ie. I have a square with an area of 36, and its sides are 6. My input proportion is 0,25. How can use this to get a rectangle of 3x12? or if my input proportions is 0,44, how can I use this to get a rectangle of 4x9? It is important that the initial area I input is the same area of the final rectangle, and that this rectangle have the same proportion I use as second input. 

Maybe this is more of maths question, but still worth giving it a shot and asking for some advice. Any help would be much appreciated. 

Thanks in advance