A path of uniform width of 5 m runs around outside a rectangular field 30 m by 25 m.Find the area of the path.

The correct answer is: Final Answer:- ∴ Area of the given path is 650 m2.

Step-by-step solution:-
From the adjacent diagram,
Let the outer rectangle represent the path around the field.
∴ Length of the outer rectangle = length of the field + 2 (width of the path)
∴ Length of the outer rectangle = 30 + 2 (5)
∴ Length of the outer rectangle = 30 + 10
∴ Length of the outer rectangle = 40 m ........................................................... (Equation i)
Also, breadth of the outer rectangle = breadth of the field + 2 (width of the path)
∴ breadth of the outer rectangle = 25 + 2 (5)
∴ breadth of the outer rectangle = 25 + 10
∴ breadth of the outer rectangle = 35 m .................................................. (Equation ii)
Area of the outer rectangle = length × breadth
∴ Area of the outer rectangle = 40 × 35 ......................................................... (From Equations i & ii)
∴ Area of the outer rectangle = 1,400 m² ............................................................ (Equation iii)
Area of the field = length × breadth
∴ Area of the room = 30 × 25 ......................................................................... (From given information)
∴ Area of the room = 750 m² .......................................................................... (Equation iv)
Now, Area of the path = Area of outer rectangle - Area of the inner field
∴ Area of the path = 1,400 - 750 ............................................................ (From Equations iii & iv)
∴ Area of the path = 650 m²
Final Answer:-
∴ Area of the given path is 650 m².