For example if your dimensions of the backgrounds were created as 2500 x 2500 pixels and you try and create at say 700 x 600 you will always get distortions. Unequal dimensions will always cause distortion when the background is of equal dimensions.

You can resize the dimensions without distortion so long as the dimensions are equal. If you go to the top menu Render/Render Settings under "General" from the box that pops up in "Dimensions" click the small arrows in "Presets" this will give you a whole list of options. There are 2 ways we can do it here if we select "Square (1.1)" this will give you equal dimensions of your first dimension as in your active view port, but what we will be looking at here if you select the "Custom" preset and type in your "Pixel Dimensions" which ever size you prefer, making sure they are equal with "Contrain Proprtions"checked. When you click accept and take a look back in the render setting you will notice it has changed to "Square (1.1)"  with your chosen dimensions still intact "Aspect Ratio" being 1.1 with "Constrain Proportions checked.

Heavenly_Spirit