Explanation:

- Start with a rectangle having length $l$ and width $w$.

- Original area = $l\times w$.

- If each side increases by 12%, new dimensions are $1.12l$ and $1.12w$.

- New area = $1.12l\times 1.12w=1.2544lw$.

- Increase in area = New area - Original area = $1.2544lw-lw=0.2544lw$.

- Percentage increase = $\left(\frac{0.2544lw}{lw}\right)\times 100\mathrm{\%}=25.44\mathrm{\%}$.

- Option 3: 25.44% is the correct answer.