Question

A pathway 2 meters wide runs outside a rectangular lawn. The lawn is 24
meters long and 16 meters broad. What is the area of the path ?
(a) 76 sq m
(b) 144 sq m
(c) 176 sq m d) None of thane​

Answer 1

Answer :

Area of the path = (c) 176 sq m

Given :

• Width of a pathway running outside of a rectangular lawn = 2 m
• Length of the rectangular lawn = 24 m
• Breadth of the rectangular lawn = 16 m

To find :

• Area of the path

Concept :

Firstly, calculate the area of the rectangular lawn by using the formula of area of rectangle. Then add twice the breadth of the path to the dimensions of the rectangular lawn, the resultant values will be the dimensions of the rectangular lawn including the path. Using those values, find the area of the rectangular lawn including the path.

To calculate the area of the path, subtract the area of rectangular lawn from the area of the rectangular lawn including the lawn.

Formula to calculate the area of the rectangle :

• Area of rectangle = l × b

where,

• l denotes the length of the rectangle

• b denotes the breadth of the rectangle

Solution :

Area of the rectangular lawn :

⠀⠀⠀⇒ Area of rectangular lawn = l × b

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Area of rectangular lawn = 24 × 16

⠀⠀⠀⇒ Area of rectanglular lawn = 384

• Area of the rectangular lawn = 384 m²

Now, calculating the dimensions of the rectangular lawn including the path :

Length of the rectangular lawn including the path :

⠀⠀⠀⇒ Length = length of rectanglular lawn + 2(width of the path)

⠀⠀⠀⇒ Length = 24 + 2(2)

⠀⠀⠀⇒ Length = 24 + 4

⠀⠀⠀⇒ Length = 28

• Length of the rectangular lawn including the path = 28 m

Breadth of the rectangular lawn including the path :

⠀⠀⠀⇒ Breadth = breadth of rectanglular lawn + 2(width of the path)

⠀⠀⠀⇒ Breadth = 16 + 2(2)

⠀⠀⠀⇒ Breadth = 16 + 4

⠀⠀⠀⇒ Breadth = 20

• Breadth of the rectangular lawn including the path = 20 m

Therefore, the length and breadth of the rectangular lawn including the path are 28 m and 20 m respectively.

Now, calculating the area of the rectangular lawn including the path :

⠀⠀⠀⇒ Area of rectangular lawn + path = l × b

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Area of rectangular lawn + path = 28 × 20

⠀⠀⠀⇒ Area of rectangular lawn + path = 560

• Area of the rectangular lawn including the path = 560 m²

Area of the path :

⠀⠀⠀⇒ Area of the path = Area of the rectangular lawn + path - Area of the rectangular lawn

⠀⠀⠀⇒ Area of the path = 560 - 384

⠀⠀⠀⇒ Area of the path = 176

Therefore,

• The area of the path = 176 m²

Answer 2

Step-by-step explanation:

Answer : ✍️

Area of the path = (c) 176 sq m

Given :

Width of a pathway running outside of a rectangular lawn = 2 m

Length of the rectangular lawn = 24 m

Breadth of the rectangular lawn = 16 m

To find : ⭐

Area of the path

Concept : ⭐

Firstly, calculate the area of the rectangular lawn by using the formula of area of rectangle. Then add twice the breadth of the path to the dimensions of the rectangular lawn, the resultant values will be the dimensions of the rectangular lawn including the path. Using those values, find the area of the rectangular lawn including the path.

To calculate the area of the path, subtract the area of rectangular lawn from the area of the rectangular lawn including the lawn.

Formula to calculate the area of the rectangle :

Area of rectangle = l × b

where,

• l denotes the length of the rectangle

• b denotes the breadth of the rectangle

Solution :

Area of the rectangular lawn :

⠀⠀⠀⇒ Area of rectangular lawn = l × b

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Area of rectangular lawn = 24 × 16

⠀⠀⠀⇒ Area of rectanglular lawn = 384

Area of the rectangular lawn = 384 m²

Now, calculating the dimensions of the rectangular lawn including the path :

Length of the rectangular lawn including the path :

⠀⠀⠀⇒ Length = length of rectanglular lawn + 2(width of the path)

⠀⠀⠀⇒ Length = 24 + 2(2)

⠀⠀⠀⇒ Length = 24 + 4

⠀⠀⠀⇒ Length = 28

Length of the rectangular lawn including the path = 28 m

Breadth of the rectangular lawn including the path :

⠀⠀⠀⇒ Breadth = breadth of rectanglular lawn + 2(width of the path)

⠀⠀⠀⇒ Breadth = 16 + 2(2)

⠀⠀⠀⇒ Breadth = 16 + 4

⠀⠀⠀⇒ Breadth = 20

Breadth of the rectangular lawn including the path = 20 m

Therefore, the length and breadth of the rectangular lawn including the path are 28 m and 20 m respectively.

Now, calculating the area of the rectangular lawn including the path :

⠀⠀⠀⇒ Area of rectangular lawn + path = l × b

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Area of rectangular lawn + path = 28 × 20

⠀⠀⠀⇒ Area of rectangular lawn + path = 560

Area of the rectangular lawn including the path = 560 m²

Area of the path :

⠀⠀⠀⇒ Area of the path = Area of the rectangular lawn + path - Area of the rectangular lawn

⠀⠀⠀⇒ Area of the path = 560 - 384

⠀⠀⠀⇒ Area of the path = 176

Therefore,

The area of the path = 176 m²