17. (10 points) As shown in the figure, Xiao Ming walks from $A$ to $B$ to $C$ to $D$, covering a total of 38 meters. Xiao Ma walks from $B$ to $C$ to $D$ to $A$, covering a total of 31 meters. What is the perimeter of the rectangle $A B C D$ in meters?
【Solution】Solution: The length of the rectangle is more than its width by: $38-31=7$ (meters), the width of the rectangle: $(38-7 \times 2) \div 3$,
$$
\begin{array}{l}
=24 \div 3, \\
=8 \text { (meters), } \\
\text { length: } 8+7=15 \text { (meters), } \\
\text { (15+8) } \times 2, \\
=23 \times 2, \\
=46 \text { (meters), }
\end{array}
$$

Answer: The perimeter of rectangle $A B C D$ is 46 meters.