Maths-
General
Easy
Question
A path of uniform width 4m runs around the outside a rectangular field 24m by 18 m.Find the area of the path ?
Hint:
Area of a rectangle = Length × breadth
The correct answer is: ∴ Area of the path is Rs. 400 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 = 24 + 2 (4)
∴ Length of the outer rectangle = 24 + 8
∴ Length of the outer rectangle = 32 m ........................................................... (Equation i)
Also, breadth of the outer rectangle = breadth of the field + 2 (width of the path)
∴ breadth of the outer rectangle = 18 + 2 (4)
∴ breadth of the outer rectangle = 18 + 8
∴ breadth of the outer rectangle = 26 m .................................................. (Equation ii)
Area of the outer rectangle = length × breadth
∴ Area of the outer rectangle = 32 × 26 ......................................................... (From Equations i & ii)
∴ Area of the outer rectangle = 832 m2 ............................................................ (Equation iii)
Area of the field = length × breadth
∴ Area of the room = 24 × 18 ......................................................................... (From given information)
∴ Area of the room = 432 m2 .......................................................................... (Equation iv)
Now, Area of the path = Area of outer rectangle - Area of the inner field
∴ Area of the path = 832 - 432 ............................................................ (From Equations iii & iv)
∴ Area of the path = 400 m2
Final Answer:-
∴ Area of the path is Rs. 400 m2.
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