question_answer 1)

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  ` 110 per \[{{\text{m}}^{\text{2}}}\].

Answer:

                (i) Area covered by the roads = Area of the rectangle PQRS + Area of the rectangle EFGH ? Area of the square KLMN \[=(\text{9}0\times \text{3}+\text{6}0\times \text{3}-\text{3}\times \text{3})\text{ }{{\text{m}}^{\text{2}}}\] \[=(\text{27}0+\text{18}0-\text{ 9})\text{ }{{\text{m}}^{\text{2}}}=\text{ 441 }{{\text{m}}^{\text{2}}}\]                 (ii) Cost of constructing the roads at the rate of ` 110 per \[~{{\text{m}}^{\text{2}}}\] ` \[441\times 110=\]` 48510