Answer: 2256

Solution: Let $D E=a$ and $E C=b$. Then the area of the rectangles $S=47(a+b)$. According to the condition, $S$ is divisible by $a$ and $b$, that is, $S=a k$ and $S=b l$, where $k=D G$ and $l=C H-$ are natural numbers. Then $a=\frac{S}{k}$ and $b=\frac{S}{l}$. We get that $S=\frac{47 S}{k}+\frac{47 S}{l}$. Therefore, $k l=47(k+l)=>$ $k l-47 k-47 l+2209=2209=>(k-47)(l-47)=2209$. Since $l<k$, that is, $l-47<k-47$. Therefore, $l-47=1$ and $k-47=2209$. Thus, $k=D G=2256$.
5. (8 points) Rectangles $A B C D, D E F G, C E I H$ have equal areas and integer sides. Find $D G$, if $B C=47$.

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