Question

2. The dimensions of a rectangular park is
100 m x 60 m. A 2 m width path made around
the rectangular park. The area (in m) of the
path is
(1) 324 (2) 656 (3) 675 (4) 780​

Answer 1

Answer:

Option (2) 656 m²

The area of the path is 656 m².

Step-by-step explanation:

Given :

Dimensions = 100 m × 60 m

Width of the path = 2 m

To find :

The area of the path

Solution :

The Rectangle formed after including the path's dimensions into the park's dimensions is the 'Bigger Rectangle'

Area of the path = Area of the bigger Rectangle - Area of the park

★ Area of the park -

• Length = 100 m
• Breadth = 60 m

⇒ Length × Breadth

⇒ 100 × 60

⇒ 6000 m²

Area of the park = 6000 m²

$\rule{300}{1.5}$

★ Area of the bigger Rectangle -

Length -

⇒ 100 + (2 + 2)

⇒ 100 + 4

⇒ 104 m

Breadth -

⇒ 60 + (2 + 2)

⇒ 60 + 4

⇒ 64 m

Area -

⇒ 104 × 64

⇒ 6656 m²

Area of the bigger Rectangle = 6656 m²

$\rule{300}{1.5}$

★ Area of the path -

⇒ 6656 - 6000

⇒ 656 m²

Area of the path = 656 m²

Therefore, the area of the path is 656 m².

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.38,2){\sf\large{64 m}}\put(9.2,0.7){\sf\large{104 m}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(8.4,2){\sf\large{60 m}}\put(9.2,1.4){\sf\large{100 m}}\put(8,1.26){\line(1,0){2.7}}\put(8.3,1){\line(0,2){1.76}}\put(10.7,1.25){\line(0,3){1.5}}\put(8.3,2.74){\line(3,0){2.4}}\put(8.04,1.07){\sf\scriptsize{2m}}\end{picture}$

$\rule{160}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\tt Area_{Path}=Outer\:Area-Inner\:Area\\\\\\:\implies\tt Area_{Path}=(L\times B)-(l\times b)\\\\\\:\implies\tt Area_{Path}=[(100+2+2)\times(60+2+2)]-(100\times60)\\\\{\scriptsize\qquad\bf{\dag}\:\:\textsf{As Width will be Added to Length and Breadth.}}\\\\:\implies\tt Area_{Path}=(104\times64)-(100\times60)\\\\\\:\implies\tt Area_{Path}=6656\:m^2-6000\:m^2\\\\\\:\implies\underline{\boxed{\textsf{\textbf{Area _{\textbf{Path}} = 656 m ^\textbf2 }}}}$

⠀

$\therefore\:\underline{\textsf{Area of Path around will be 2) \textbf{656 m ^\textbf2 }}}.$