2. Divide a square into 25 smaller squares, where 24 of the smaller squares are unit squares, and the remaining piece can still be cut into some squares with a side length of 1. Try to find the area of the original square. ${ }^{\text {[2] }}$
(1997, Global City Mathematics Competition (Junior Group))
Let the original side length of the square be $a$, and the side length of the remaining square be $b$.
According to the problem, $a$ and $b$ are both positive integers.
Thus, $a^{2}-b^{2}=24$, and we only need to solve this indeterminate equation.
The solutions are $\left\{\begin{array}{l}a=7 \\ b=5\end{array}\right.$ or $\left\{\begin{array}{l}a=5, \\ b=1\end{array}\right.$ (discard).
Therefore, the area is 49.