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

              (i) the area covered by the roads.

Answers (1)

It is given that the width of each road is 3m and 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 total park is 

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

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

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

Area of road parallel to 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              

Therefore, the area of road is  441 \ m^2

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