Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the center of the field. If the width of each road is 3 m,
Find:
(i) The area covered by the roads.
(ii) The cost of constructing the roads at the rate of Rs. 110 per m2.
(i) It is given in the question that,
Length of field = 90 m
Breadth of field = 60 m
We know that,
Area of rectangle = Length × Breadth
∴ Area of field = 90 × 60
= 5400 m2
Also, we have
Length of road PQRS = 90 m
Length of road ABCD = 60 m
Width of each road = 3 m
∴ Area of the roads = Area of (PQRS) + Area of (ABCD) – Area of (KLMN)
= (90 × 3) + (60 × 3) – (3 × 3)
= 270 + 180 – 9
= 450 – 9
= 441 m2
(ii) It is also given in the question that,
Cost of constructing 1 m2 of road = Rs 110
∴ Cost of constructing 441 m2 road = 110 × 441
= Rs 48510