A rectangular lawn 70m by 50m has two roads each 5m wide,running through its middle .One parallel to its length and other parallel to its breadth . Find the cost of constructing the roads at ₹120 per m^2
Answers
Area of the road parallel to the breadth= 50m×5m=250m^2
Area of the portion of the road overlapping= 5m×5m=25m^2
Total area of the road= (350m^2 + 250m^2)- 25m^2 = 575m^2
Cost of construction= 120×575= Rs. 69,000
Given,
A rectangular lawn of length 70 m and breadth 50 m.
Two roads of breadth 5 m are passing through its middle.
One road is parallel to the length of the lawn and the other is parallel to its breadth.
Cost of constructing the roads = Rs. 120 per m².
To find,
The cost of constructing the roads.
Solution,
The cost of constructing the roads at Rs. 120 per m² will be Rs. 69,000.
We can easily solve this problem by following the given steps.
To find the cost of the construction of the roads, first, we will have to find their area.
Now, we know that there will be only one centre of the lawn. So, the two roads will be overlapping each other.
Let's first find the area of the road parallel to the length of the lawn.
Length of the road (l) = 70 m
The breadth of the road = 5 m
Area of the road (A1) = length × breadth
A1 = (70×5) m²
A1 = 350 m²
Now, let's first find the area of the road parallel to the breadth of the lawn.
Length of the road = 50 m
The breadth of the road = 5 m
Area of the road (A2) = length × breadth
A2 = (50×5) m²
A2 = 250 m²
Now, the overlapping area at the centre will be a square with all sides being equal.
Side = 5 m
Area of the square (A3) = side × side
A3 = (5×5) m²
A3 = 25 m²
Now, the total area of the two roads (A) = (A1 + A2) - A3
A = (350+250) - 25
A = 600 - 25
A = 575 m²
The cost of the construction of roads at Rs. 120 per m² (C)= A × 120
C = Rs. (575×120)
C = Rs. 69,000
Hence, the cost of constructing the roads at Rs. 120 per m² is Rs. 69,000.