Question

A rectangular garden has dimensions 11 mx 8m. A path of 2 m wide has to
constructed along its sides. Find the area of the path.​

Answer 1

If a 2 m wide path is built along the sides of a rectangular garden of 11 m X 8 m then the area of the path is 92 m².

Step-by-step explanation:

Step 1:

The length of the garden = 11 m

The breadth of the garden = 8 m

∴ Area of the rectangular garden ABCD = l * b = 11 * 8 = 88 m²

Step 2:

A path of 2 m wide run along the sides of the rectangular garden  

So,  

The length of the rectangle EFGH = l + 2w = 11 + (2*2) = 15 m

The breadth of the rectangle EFGH = b + 2w = 8 + (2*2) = 12 m

∴ Area of the rectangular garden including the path EFGH = l * b = 15 * 12 = 180 m²

Step 3:

Thus,  

The area of the path is given by,

= [Area of the rectangular garden including the path EFGH] – [Area of the rectangular garden ABCD]  

= 180 – 88

= 92 m²

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Answer 2

GIVEN:

A rectangular garden of length=11m, width=8m

The path to be constructed of 2m wide

TO FIND:

The area of the path

SOLUTION:

After the construction of the path, the rectangular field is changed into two rectangular fields the one is the outer boundary of the field and the other is an inner boundary with length=7m and width=4m

The area of the outer rectangular boundary is

$area=length*width\\area=11m*8m\\area=88m^{2}$

the area of an inner rectangular field formed due to the construction of the path is

$area=length*width\\area=7m*4m\\area=28m^{2}$

The area of the path=the area of the outer rectangular field - the area of the inner rectangular field

The area of the path$=88m^{2} -28m^{2} \\=60m^{2}$

Hence, the area of the path is $60m^{2}$​