# Q. 7.     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            (ii) the cost of constructing the roads at the rate of  $Rs. 110\; per\; m^{2}$.

R Riya

It is given that the width of each road is $3m$ and the length of rectangular park is $90\; m$ and breadth is $60\; m$

Now, We know that area of rectangle is = $length \times breadth$

Area of the total park is

$\Rightarrow 90 \times 60 = 5400 \ m^2$                   -(i)

Area of road parallel to the width of the park ( ABCD ) is

$\Rightarrow 60 \times 3 = 180 \ m^2$                           -(ii)

Area of road parallel to the length of park ( PQRS )  is

$\Rightarrow 3 \times 90 = 270 \ m^2$                          -(iii)

The common area of both the roads ( KMLN ) is

$\Rightarrow 3 \times 3 = 9 \ m^2$                               -(iv)

Area of roads = $[(ii)+(iii)-(iv)]$

$\Rightarrow 180+270-9 = 441 \ m^2$

Now, the cost of constructing the roads at the rate of  $Rs. 110\; per\; m^{2}$ is

$\Rightarrow 441 \times 110 = 48510 \ Rs$

Therefore, the cost of constructing the roads at the rate of  $Rs. 110\; per\; m^{2}$ is $Rs \ 48510$

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