RAS question
A rectangular garden 60 m × 40 m has a path of width 2 m all around it. The area of the path is:
Correct answer: (D) 416 m².
The area of the 2 m wide path around a 60 m by 40 m rectangular garden is 416 m².
Explanation
NCERT states the rectangle area rule as length × breadth, and its perimeter-and-area examples use the same outer-area minus inner-area method for paths around rectangular figures. Here, the path is 2 m wide on every side of the garden, so it adds 4 m to each dimension: the outer rectangle is 64 m by 44 m. Its area is 64 × 44 = 2816 m². The original garden area is 60 × 40 = 2400 m². The path is only the part outside the garden but inside the outer rectangle, so its area is 2816 − 2400 = 416 m².
Why the other options are wrong
- (A) 408 m² is too small because it does not come from the required outer rectangle of 64 m by 44 m.
- (B) 400 m² treats the border too roughly and ignores that the path adds 2 m on both sides of both dimensions.
- (C) 480 m² overcounts the border area; the correct subtraction is 2816 m² − 2400 m², not a larger difference.
Concept
This tests mensuration: finding the area of a rectangular path by subtracting the inner rectangle from the outer rectangle. It recurs in RAS reasoning because a simple area formula must be paired with careful reading of width on all sides.