Question

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 centre of the fields. If the width of each road is 3 m, find

1)the area covered by the roads.

2) the cost of constructing the roads at the rate of Rs 110 per m².

Answer 1

Length (l) of field = 90 m

Breadth (b) of field = 60 m

Area of field = 90 × 60 = 5400 m²

Length of road PQRS = 90 m

Length of road ABCD = 60 m

Width of each road = 3 m

Area of the roads = ar (PQRS) + ar (ABCD) − ar (KLMN)

= (90 × 3) + (60 × 3) − (3 × 3)

= 270 + 180 − 9 = 441 m²

Cost for constructing 1 m² road = Rs 110

Cost for constructing 441 m² road = 110 × 441 = Rs 48510