A 60-meter length and 40-meter width make up a rectangle garden. It is intended to build two 4-meter-wide crosswalks that run parallel to the garden’s edges. These trails go through the garden’s middle. Calculate the two pathways’ construction costs at a rate of ₹70 per square meter. [Answer Limit: 250 words] [UKPSC 2012]
To find the cost of constructing the two cross paths in the rectangular garden, we first need to determine the area of these paths.
Dimensions of the Garden:
Dimensions of the Paths:
Each path is 4 metres wide and they are constructed parallel to the sides of the garden, passing through the center.
Area of the Paths:
Area of Vertical Path=Width×Length=4×40=160 square metres
Area of Horizontal Path=Width×Length=4×60=240 square metres
Total Area of the Paths:
Since the paths overlap in the center, we need to subtract the area of the overlapping section (which is a square of side 4 metres):
Area of Overlap=4×4=16 square metres
Total Area of Paths:
Total Area=Area of Vertical Path+Area of Horizontal Path−Area of Overlap Total Area=160+240−16=384 square metres
Cost of Construction:
Given the cost per square metre is ₹70:
Total Cost=Total Area×Cost per square metre=384×70=₹26,880
Conclusion:
The cost of constructing the two paths is ₹26,880.