Question

rectangular field 90m long and 70m wide has a 3m wide path inside along the sides of the field.
Find the area of the path and the cost of its construction at the rate of Rs 20 per 10m2.​

Answer 1

Given :

• Dimensions of the rectangular field :-

• Length of the rectangular field = 90 m
• Breadth of the rectangular field = 70 m
• Width of a path constructed along the sides of the field = 3 m

To find :

• Area of the path
• Cost of its construction at the rate of Rs. 20 per 10 m²

Knowledge required :-

• Formula of area of rectangle :-

⠀⠀⠀⠀⠀⠀Area of rectangle = l × b

where,

• l is the length of the rectangle
• b is the breadth of the rectangle

Solution :

Firstly, we will find the area of the rectangular field :-

⠀⠀⠀⇒ Area of rectangular field = l × b

⠀⠀⠀⇒ Area = 90 × 70

⠀⠀⠀⇒ Area = 6300

Area of the rectangular field = 6300 m²

Dimensions of the rectangular field including the path :-

→ Length of the rectangular field including the path = 90 + 3 + 3 = 96 m

→ Breadth of the rectangular field including the path = 70 + 3 + 3 = 76 m

Area of the rectangular field including the path :-

⠀⠀⠀⇒ Area = 96 × 76

⠀⠀⠀⇒ Area = 7296

Area of the rectangular field including the path = 7296 m²

Area of the path = Area of the rectangular field including the path - Area of the rectangular field

⠀⠀⠀⇒ Area of path = 7296 - 6300

⠀⠀⠀⇒ Area of path = 996

★ Area of the path = 996 m²

Cost of its construction at 10 m² = Rs 20

Cost of its construction at 1 m² = 20/10 = Rs. 2

Cost of constructing 996 m² of path = rate × area

⠀⠀⠀⇒ Cost = 996 × 2

⠀⠀⠀⇒ Cost = 1992

★ Cost of the construction of the path = Rs. 1,992