4. In a rectangular flower bed, install two identical sprinklers so that the entire flower bed can be watered. It is known that the watering area of each sprinkler is a circle with a radius of $10 \mathrm{~m}$. How should it be designed (find the distance between the two sprinklers and the length and width of the rectangle) to maximize the area of the rectangular flower bed?
(The answer: The sides of the rectangular flower bed are designed to be $10 \sqrt{2} \mathrm{~m}$ and $20 \sqrt{2} \mathrm{~m}$, at which point the area of the flower bed is maximized.)