Java: maintaining aspect ratio of JPanel background image

I have a JPanel with a painted background image and a layout manager holding other smaller images, all of this inside a JFrame. The background image is pretty big and I want to be able to have it maintain its aspect ratio whether its on a big or small monitor.

Eventually, I want to be able to have my LayoutManager and the smaller images in its cells "glued" to the background picture.

I looked around for resources and it seems that many examples use a BufferedImage but I am not; will this pose a problem? I'll post my code below for painting the image, If I lack any information please let me know.

public class MonitorPanel extends JPanel {
    Image img;
    public MonitorPanel() throws MalformedURLException {
        //add components

        try {
            img = ImageIO.read(new File("src/customer_vlans.jpg"));
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }

    }
protected void paintComponent(Graphics g)
{
    //paint background image
    super.paintComponent(g);
    //g.drawImage(img, 0, 0, getWidth(), getHeight(), this);
    g.drawImage(img, 0, 0, this);

}

}

EDIT: I should mention that I know the aspect ratio formula: original height / original width x new width = new height However, I do not know how to use that correctly to my advantage.