Question

2. A path of uniform width 3m, runs around the inside of the rectangular field 30 m by
27 m. Find the area of the path.
[3]​

Answer 1

⛦ Given :

• Width of the path = 3m
• Length of the rectangular field = 30m
• Breadth of the rectangular field = 27m

⛦ To find :

• The area of the path.

⛦ Solution :

First ,we will find the area of the rectangular field.

Area of rectangle = length × breadth

A/Q

Area of field = 30 × 27

Area of field = 810 m²

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Now, width of the path(given) = 3 m

We will find the area of rectangular field without including path.

So,

• Length of field without including path

= 30 - (3 + 3)

= 30 - 6

= 24 m

• Breadth of field without including path

= 27 - (3 + 3)

= 27 - 6

= 21 m

Thus area of field without including path

= 24 × 21

= 504 m²

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Thus,

★The area of path = Area of whole field - area of field without including path

Area of path = 810 - 504

Area of path = 306 m²

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Answer 2

Question :-

A path of uniform width 3m, runs around the inside of the rectangular field 30 m by

27 m. Find the area of the path??

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Given:-

$length \: = 30m \\ breadth \: = 27m \\ width = 3m$

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Find:-

Area Of path.

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Solution:-

Firstly, We Find The Area Of Rectangular Field and then We Find the Area Of Path.

So,

$Area \:Of \:rectangle \longmapsto \: l \times b \\ \longmapsto \: 30 \times 27 \\ \longmapsto {810m}^{2}$

Now,

We Will find the area of rectangular field without including the area of path..

So,

$length \: of \: the \:rectangluar \: field \: without \: including \: path \\ \longmapsto \:( lenght \: of \: total \: area )\: -( lenght \: of \: path) \\ \longmapsto \: 30 - (3 + 3) \\ \longmapsto \: 30 - 6 \\ \longmapsto \: 26m$

$breadth \: of \: the \:rectangluar \: field \: without \: including \\ breadth \: of \: path \\ \longmapsto \:( breadth \: of \: total \: area )\: -( breadth\: of \: path) \\ \longmapsto \: 27 - (3 + 3) \\ \longmapsto 27 - 6 \\ \longmapsto21 m$

Now, We Can easily find the area of the given path..

$area \: of \: the \: path \: \longmapsto \: 26 \times 21 {m}^{2} \\ \longmapsto {504m}^{2}$

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Final Answer:-

Thus, The area of the given path is

$\longmapsto {504m}^{2}$

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