Question

• A rectangular grassy plot is 75 m long and 60 m broad. It has a path of width 2 m all around
it on the inside. Find the area of the path and the cost of constructing it at 125 per m²​

Answer 1

Step-by-step explanation:

Area of the plot along with the path is

l x b

(75+2+2) x (60+2+2)

79 x 64

5056m^2

Area of the plot is

l x b

75 x 60

4500m^2

Area of the path is

5056-4500

= 556 m^2

The cost of constructing the path is

125 x 556

59500 RS

Answer 2

Given :

• Length of rectangular grassy plot = 75 m

• Breadth of rectangular grassy plot = 60 m

• Width of path around it on the inside = 2 m

• Cost of constructing per m² = Rs. 125

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To Find :

• Area of path = ?

• Total cost of constructing the path = ?

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Solution :

As, we know that :

$\large \underline{\boxed{\bf{ Area \: of \: rectangle = length \times breadth }}}$

$\sf : \implies Area \: of \: rectangular \: grassy \: plot = 75 m \times 60 m$

$\sf : \implies Area \: of \: rectangular \: grassy \: plot = 4500 m^{2}$

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Now, we have

• Width of path = 2 m

Hence,

Length of (plot + path) = 75 m + 2 m = 77 m

Breadth of (plot + path) =60+2=62m

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So,

$\sf : \implies Area \: of \: (plot + path) = 77m \times 62 m$

$\sf : \implies Area \: of \: (plot + path) = 4774m^{2}$

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Now, we have :

Area of path = Area of (plot + path) − Area of plot

Therefore,

Area of path = 4774 m² − 4500 m² = 274 m²

∴ Area of path is 274 m²

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Now, we are given cost of constructing path is Rs.125 per m².

Therefore,

Cost of constructing path of width 2 m around the plot = Rs. 125 × Area of path

= Rs. 125 × 274

= Rs. 34250

∴ Cost of constructing path of width 2 m around the plot is Rs. 34250.