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Fundamental Idea About Rectangular Pathways:

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) \(=\) $l\times b$ \(sq. units\).

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 \(=\) The area of the outer rectangle \(–\) The area of the inner rectangle

**The area of the rectangular pathway**

**is**$(\mathit{LB}-\mathit{lb})\phantom{\rule{0.147em}{0ex}}$\(sq. units\)