a rectangular lawn 80*60m has two roads each 10m wide running in the middle of it,one parallel to the length and the other parallel to the breadth.find the cost of graveling them at ₹1.20 per square metre
FOR RECTANGULAR LAWN.
Length, L = 80m.
Breadth, B= 60m.
For Vertical road:
length= Breadth of rectangle
length = 60m.
Breadth = 10m.
Thus, Area of vertical road
=length × breadth
= 60m ×10m
=600m².
For Horizontal road:
length = length of rectangle.
length = 80m
breadth= 10m.
Thus, area of horizontal road
= length ×breadth
= 800m × 10m
=800m².
Note: The roads overlap in the middle of rectangle and form a square having side of 10m.
FOR SQUARE:
Area of square = Side × Side
Area of square = 10m × 10m
Area of square = 100m².
Therefore,
Area needd of road to be gravel
= Area of vertical road + area of horizontal road - area of square
= 600m² + 800m² -100m²
= 1300m².
If the cost of gravelling for 1m² = Rs 1.20
So, Cost of gravelking for 1300m²
= 1300 ×Rs 1.20
=Rs 1,560. Ans.
Good
To find the cost of gravelling the two roads, we need to find their areas first.
The length of the rectangular lawn is 80 meters and there is a road running parallel to the length, which is 10 meters wide. Therefore, the length of the road is also 80 meters.
The breadth of the rectangular lawn is 60 meters and there is a road running parallel to the breadth, which is 10 meters wide. Therefore, the breadth of the road is also 60 meters.
The area of the road parallel to the length can be found by multiplying the length of the road (80m) by its width (10m):
Area of the road parallel to the length = 80m * 10m = 800 square meters.
The area of the road parallel to the breadth can be found by multiplying the breadth of the road (60m) by its width (10m):
Area of the road parallel to the breadth = 60m * 10m = 600 square meters.
Now, we can calculate the cost of gravelling both roads by multiplying their respective areas by the cost per square meter:
Cost of gravelling road parallel to the length = Area of road parallel to the length * Cost per square meter
= 800 square meters * ₹1.20 per square meter
= ₹960.
Cost of gravelling road parallel to the breadth = Area of road parallel to the breadth * Cost per square meter
= 600 square meters * ₹1.20 per square meter
= ₹720.
Therefore, the cost of gravelling both roads is ₹960 + ₹720 = ₹1680.
To find the cost of graveling the roads, we need to calculate the area of each road and then multiply it by the cost per square meter.
1. Calculate the area of the road parallel to the length:
The width of the road is given as 10m, and the length of the lawn is 80m. Since the road runs in the middle of the lawn, the length of the road is also 80m. The area of this road is therefore obtained by multiplying the length and width: 80m * 10m = 800 square meters.
2. Calculate the area of the road parallel to the breadth:
The width of the road is given as 10m, and the breadth of the lawn is 60m. Since the road runs in the middle of the lawn, the length of the road is also 60m. The area of this road is obtained by multiplying the length and width: 60m * 10m = 600 square meters.
3. Add the areas of both roads to get the total area that needs to be gravelled: 800 square meters + 600 square meters = 1400 square meters.
4. Finally, multiply the total area by the cost per square meter to find the cost of graveling the roads:
1400 square meters * ₹1.20 = ₹1680.
Therefore, the cost of graveling the roads at ₹1.20 per square meter is ₹1680.