$36 \cdot 37$ As shown in the figure, along the sides of a square with a side length of 90 meters, in the direction $A$ $\rightarrow B \rightarrow C \rightarrow D \rightarrow A \rightarrow \cdots$, person A starts from $A$ at a speed of 65 meters/min, and person B starts from $B$ at a speed of 72 meters/min. When B catches up with A for the first time, they are on the
(A) $A B$ side.
(B) $B C$ side.
(C) $C D$ side.
(D) $D A$ side.
[Solution] From the problem, we know that Yi walks 72 - 65 = 7 meters more per minute than Jia. Initially, Yi is 90 \cdot 3 = 270 meters behind Jia. When Yi catches up with Jia for the first time, Yi has walked 72 \cdot \frac{270}{7} = \frac{72}{7} \cdot \frac{3}{4} \cdot 360 = \frac{54}{7} \cdot 360 = 7 \cdot 360 + \frac{5}{7} \cdot 360, and \quad \frac{5}{7} \cdot 360 = \frac{1800}{7} \approx 257,
which means Yi has walked 7 laps plus 257 meters, and catches up with Jia for the first time on DA. Therefore, the answer is (D).