Question

Through a rectangular filed 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 in. Find :

(i) The area covered by the roads.

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

Answer 1

(i) The area covered by the roads.

Area covered by the roads = Area of klmn + Area of abcd – Area of 1, 2, 3, 4

Area of abcd = 90 × 3 = 270 sq m

Area of klmn = 60 × 3 = 180 sq m.

Area of 1, 2, 3, 4 = \({3\times3}={9\;sq\;m}\)

= 180 + 270 – 9 = 441 sq m.

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

Cost of constructing the roads = Rs 110/sq m

∴ Total cost of constructing the roads

= 441 × 110 = Rs. 48.510