Question

1. A garden is 100 m long and 60 m broad. A path 3 m wide is to be built outside it. Find the area of the path.​

Answer 1

Answer :-

Area of the path = 996 m²

$\rule{150}2$

Consider ABCD as the rectangular park having -

• AB = CD = length of rectangular park = 100 m
• BC = AD = breadth of rectangular park = 60 m

Now,

Area of rectangle = length × breadth

Area of park = Area of rectangle

=> 100 × 60

=> 6000 m² ....(1)

Also, a path which is 3 m wide; but outside the park.

So,

→ New length = 100 + 3(2)

=> 100 + 6

=> 106 m

→ New breadth = 60 + 3(2)

=> 60 + 6

=> 66 m

→ New area of park = 106 × 66

=> 6996 m² ....(2)

Area of the path = New area of the park - Area of the park

Substitute the known values above

=> (6996 - 6000) m²

=> 996 m²

Answer 2

Answer:

Area of path » 996 m²

Step-by-step explanation:

Given :

The length of the of the garden is 100 m and its breadth is 60 m.

In this question, it is simply given that we have to find the area of the path only, and the path is 3 m wide from all sides.

So, for the solution, we have to find the area of the inner rectangle or the ground, and the area of the whole rectangle or the ground including the path.

So,

Area of the inner rectangle or the area of the ground :

› Length * Breadth

=  100 * 60

= 6000 m²

Now, we'll find the area of the ground including the path, but for that we have to find the length and breadth.

Length including 3 m path from both sides :

100 + ( 3 + 3 )  = 160 m

Breadth including 3 m path from both sides :

60 + ( 3 )2 = 66 m

Now, we can find the area of the whole ground including the path.

› Length * Breadth

= 106 * 66

= 6996 m²

Area of path = Area of the ground including path - Area of ground excluding path

» Area of path = 6996 - 996

» 996 m²