A rectangular garden is 60 metres long and 40 metres wide. Two cross paths, each 4 metres wide, are to be constructed parallel to the sides of the garden. These paths pass through the centre of the garden. Find the cost of construction of the two paths at the rate of ₹70 per square metre.

Points to Remember:

• Area of a rectangle = length × width
• Calculation of overlapping area
• Cost calculation based on area and rate

Introduction:

This question involves calculating the area of two intersecting paths within a rectangular garden and determining the total cost of construction based on a given rate. The problem requires a clear understanding of area calculations and the ability to handle overlapping regions. We are given a rectangular garden with dimensions 60 meters by 40 meters. Two perpendicular paths, each 4 meters wide, intersect at the center of the garden. We need to find the total area of these paths and then calculate the construction cost at ₹70 per square meter.

Body:

1. Calculating the Area of the Paths:

The garden is 60m long and 40m wide. Two paths, each 4m wide, run parallel to the sides and intersect at the center.

• Path 1 (parallel to length): This path has a length of 60m and a width of 4m. Its area is 60m × 4m = 240 sq m.

• Path 2 (parallel to width): This path has a length of 40m and a width of 4m. Its area is 40m × 4m = 160 sq m.

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• Overlapping Area: The two paths intersect, creating an overlapping square area at the center of the garden. This square has sides of 4m each. The area of the overlap is 4m × 4m = 16 sq m.

• Total Area of Paths: To avoid double-counting the overlapping area, we subtract the overlapping area from the sum of the individual path areas: (240 sq m + 160 sq m) – 16 sq m = 384 sq m.

2. Calculating the Construction Cost:

The cost of construction is ₹70 per square meter. Therefore, the total cost for constructing the two paths is:

384 sq m × ₹70/sq m = ₹26,880

Conclusion:

The total area of the two intersecting paths in the rectangular garden is 384 square meters. Considering the overlapping area, the cost of constructing these paths at a rate of ₹70 per square meter amounts to ₹26,880. This calculation demonstrates a practical application of area calculations involving overlapping regions. This problem highlights the importance of accurate area calculations in real-world applications such as construction projects. Efficient planning and accurate estimations are crucial for effective resource management and cost control in such projects. Further, incorporating sustainable materials and environmentally friendly construction practices would enhance the project’s overall value and contribute to a more holistic approach to development.

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