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:

(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)Here, PQ = 3 m and PS = 60 m, EH

= 3 m and EF = 90 m and KL = 3 m and KN = 3 m Area of roads

= Area of PQRS + Area of EFGH – Area of KLMN

[∵ KLMN is taken twice, which is to besubtracted]

= PS x PQ + EF x EH – KL x KN

= (60 x 3) + (90 x 3) – (3 x 3)

= 180 + 270 – 9

= 441 m2

(ii) The cost of 1 m2 constructing the roads = Rs 110

The cost of 441 m2 constructing the roads

=Rs 110 x 441 =Rs 48,510

Therefore, the cost of constructing the roads = Rs 48,510