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 m^{2} ............................................................ (Equation iii)

Area of the field = length × breadth

∴ Area of the room = 24 × 18 ......................................................................... (From given information)

∴ Area of the room = 432 m^{2} .......................................................................... (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 m^{2}

Final Answer:-

∴ Area of the path is Rs. 400 m^{2}.

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