Illustrate a square divided into nine rectangles. It is known that rectangle $E$ is actually a square, and the areas of rectangles $A, B, C$ are $18 \mathrm{~cm}^{2}$, $63 \mathrm{~cm}^{2}$ and $189 \mathrm{~cm}^{2}$, respectively. Find the perimeter of rectangle $D$.

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Geometry, Perimeter and Area, Ratio.
Since the entire figure is a large square, and $E$ is also a square;
Therefore, $A 、 B 、 C 、 D$ can be combined to form a square.
Since $S_{\text {rectangle } A} \times S_{\text {rectangle } C}=S_{\text {rectangle } B} \times S_{\text {rectangle } D}$;

Therefore, $S_{\text {rectangle } D}=S_{\text {rectangle } A} \times S_{\text {rectangle } C} \div S_{\text {rectangle } B}=18 \times 189 \div 63=54$ square centimeters;
The area of the square formed by $A 、 B 、 C 、 D$ is $18+63+189+54=324$ square centimeters, with a side length of 18 centimeters; the ratio of the length of rectangle $D$ to the length of rectangle $C$ is $54: 189=2: 7$;
The length of rectangle $D$ is $18 \times \frac{2}{2+7}=4$ centimeters;
The ratio of the width of rectangle $D$ to the width of rectangle $A$ is $54: 18=3: 1$;
The width of rectangle $D$ is $18 \times \frac{3}{3+1}=13.5$ centimeters;
The perimeter of rectangle $D$ is $(4+13.5) \times 2=35$ centimeters.