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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 center of the fields. If the width of each road is 3 m, the area covered by the roads is ____ m 2 .

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Detailed Solution

 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 center of the fields. If the width of each road is 3 m, the area covered by the roads is 441 m 2 .
Given a rectangular field of length 90 m and breadth 60 m.
Area of path 1 is,
=Length×Breadth
=90m×3 m =270 m 2
Area of path 2 is,
=Length×Breadth
=60m×3 m =180 m 2
Since the area of intersection is common in both path, we have to consider it only once
Area of center region is,
=side×side
=3m×3m =9 m 2
Now, the area covered by both paths is,
= area of path 1 + area of path 2 – area of central region
= 270 + 180 – 9
= 441 m 2 Therefore, area covered by roads is 441 m 2 .
 
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