Rectangle pathways — lesson. Mathematics State Board, Class 7.

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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

$(LB - lb)$

$sq. units$

Did you find an error?

2. Rectangle pathways