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Fundamental Idea About Rectangular Pathways:
![shutterstock_1770088112.jpg](https://resources.cdn.yaclass.in/772ca0c1-b179-409b-9fe3-d07f8d426d4f/shutterstock1770088112w465jpg.jpg)
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.
![outer inner rectangle (1).png](https://resources.cdn.yaclass.in/0fb287e1-bb60-434d-a8fb-f0574acf74ac/outerinnerrectangle1w658png.png)
Let \(l\) and \(b\) be the length and breadth of the park.
Area of the park (inner rectangle) \(=\) \(sq. units\).
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