Theory:

Consider a rectangular park, as shown in the above figure. A uniform path is to be laid outside the park. How do we find the area of the path?

The uniform path, including the park, is also a rectangle. If we consider the path as the outer rectangle, then the park will be the inner rectangle.

Let $$l$$and $$b$$ be the length and breadth of the park.
Area of the park (inner rectangle) $$=$$ $l×b$  sq. units.
Let $$w$$ be the width of the path. If $$L$$, $$B$$ are the length and breadth of the outer rectangle, then
$$l = L+ 2w$$ and $$b = B + 2w$$.

Similarly for inner rectangle $$l = L - 2w$$and $$b = B - 2w$$

Therefore,
The area of the rectangular pathway $$=$$ Area of the outer rectangle $$–$$ Area of the inner rectangle
The area of the rectangular pathway is $\left(\mathit{LB}-\mathit{lb}\right)\phantom{\rule{0.147em}{0ex}}$ $$sq. units$$