A rectangular plot of lawn shown in the figure has dimensions x and y and is surrounded by a gravel pathway of width 2 m. What is the total area of the pathway ?

examrobotsa's picture

Submitted by examrobotsa on

Q: 130 (IAS/1997)
A rectangular plot of lawn shown in the figure has dimensions x and y and is surrounded by a gravel pathway of width 2 m. What is the total area of the pathway ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,4,0,4,0,3

keywords: 

{'total area': [1, 1, 0, 0], 'gravel pathway': [0, 1, 0, 0], 'rectangular plot': [0, 1, 0, 0], 'lawn': [0, 1, 0, 0], 'pathway': [0, 1, 0, 0], '4y': [0, 2, 0, 0], 'width': [0, 2, 1, 1]}

The area of the pathway is calculated by subtracting the area of the lawn (length x breadth = x*y) from the total area (x+4)(y+4), as the pathway goes 2m outside on all sides. The correct formula to use would be (x+4)(y+4) - (x*y).

Option-1, 2x + 2y + 4, and option-2, 2x + 2y + 8, are essentially same, just with different constants added. They are incorrect as they do not consider the total and lawn areas.

Option-3, 4x+ 4y + 8, misses out on the dimensions to the other two sides of the lawn along y-axis making it incorrect.

Option-4, 4x + 4y + 16, correctly applies the formula. First, calculate the total area including the pathway (x+4)(y+4), which is x*y + 4x + 4y +16, then subtract the area of the lawn x*y. This leaves us with 4x + 4y +16, which is the total area of the pathway. So, the correct answer is option-4.