Question

Through a rectangular field of length 100m and breadth 50m,two roads are constructed which are parallle to the sides and cut each other at right angles through the centre of the field. If the width of road parallel to length is 2m and the width of road parallel to breadth is 5m, find the area covered by the roads.

1

Answer 1

Given:

Through a rectangular field of length 100m and breadth 50m

Two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the field.

If the width of road parallel to length is 2m and the width of road parallel to breadth is 5m

To find:

The area covered by the roads

Solution:

We know that the formula of an area of a rectangle is:

$\boxed{\bold{Area\:of\:a \:rectangle = length \times breadth}}$

The dimensions of the rectangular field ABCD:

Length = 100 m

Breadth = 50 m

We will find the area of the road whose width is 2 m and is parallel to the length of the rectangular field,

Area of road EFGH = length × width = 100 × 2 = 200 m²

We will also find the area of the road whose width is 5 m and is parallel to the breadth of the rectangular field,

Area of road IJLK = breadth × width = 50 × 5 = 250 m²

There is a common portion which is formed by the intersection of the two roads, so

Area of the common portion MNPO = 2 × 5 = 10 m²

Now,

The area of the two roads will be given by,

= [Area of EFGH] + [Area of IJLK] - [Area of MNPO]

= 200 m² + 250 m² - 10 m²

= 450 m² - 10 m²

= 440 m²

Thus, the area covered by the two roads is → 440 m².

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