[hardwired]

The trick is to base your variable values on the current size of the component.

Code:

import java.awt.*;
import javax.swing.*;

public class StretchyGraphics extends JPanel {
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                            RenderingHints.VALUE_ANTIALIAS_ON);
        int w = getWidth();
        int h = getHeight();
        g2.drawRect(w/16, h/16, w*7/8, h*7/8);
    }

    public static void main(String[] args) {
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.getContentPane().add(new StretchyGraphics());
        f.setSize(400,400);
        f.setVisible(true);
   }
}