Q

# 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. (i) the area covered by the roads

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.

Views
R

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  $441 \ m^2$

Exams
Articles
Questions