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  • 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. (ii) the cost of constructing the roads

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 the cost of constructing the roads at the rate of Rs. $110$ per $\mathrm{m}^2$.

 

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It is given that the width of each road is 3 m and the length of rectangular park is 90 m and breadth is 60 m Now, We know that the area of a rectangle is =length $\times$ breadth
The area of the total park is
$\Rightarrow 90 \times 60=5400 \mathrm{~m}^2$
The area of road parallel to the width of the park (PQRS) is
$\Rightarrow 60 \times 3=180 \mathrm{~m}^2$
The area of road parallel to the length of the park (EFGH) is
$\Rightarrow 3 \times 90=270 \mathrm{~m}^2$
The common area of both the roads (KLMN) is
$\Rightarrow 3 \times 3=9 m^2$
$\text { Area of roads }=[(i i)+(i i i)-(i v)]$
$\Rightarrow 180+270-9=441 \mathrm{~m}^2$

Now, the cost of constructing the roads at the rate of Rs. $110$ per $\mathrm{m}^2$ is
$\Rightarrow 441 \times 110=48510$ Rs
Therefore, the cost of constructing the roads at the rate of Rs. $110$ per $\mathrm{m}^2$ is Rs. $48510$.

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