Question

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

Answer 1

Answer:

Length of plot =75m

Breadth of plot =60m

Area of plot =l×b

=75×60=4500m

2

Now,

Width of path =2m

Therefore,

Length of plot including path =75+2=77m

Breadth of plot including plot =60+2=62m

Therefore,

Area of plot including plot =77×62=4774m

2

Therefore,

Area of path = Area of plot including path − Area of plot only

∴ Area of path =4774−4500=274m

2

Given that cost of constructing path is Rs.125 per square meter.

Therefore,

Cost of constructing path around plot=125×274=Rs.34250.

Answer 2

Given :-

Length of the grassy plot = 75 m

Breadth of the grassy plot = 60 m

Width of the path inside = 2 m

Cost of constructing er meter = Rs. 125

To Find :-

The area of the rectangular grassy plot.

The cost of constructing the path.

Analysis :-

Find the area of the rectangular grassy plot.

Then add the width of the path to the length and the breadth given.

Find the area of the path including the path.

Next subtract the area of the grassy plot from the the new area including the path to get the area of the path.

Multiply the cost of constructing per meter to the area of the path.

Solution :-

We know that,

• l = Length
• b = Breadth
• w = Width
• a = Area

Given that,

Length (l) = 75 m

Breadth (b) = 60 m

Width of the path (w) = 2 m

By the formula,

$\underline{\boxed{\sf Area \ of \ a \ rectangle=Length \times Breadth}}$

Substituting their values,

Area = $\sf 75 \times 60$

$\longrightarrow \sf 4500 \ m^{2}$

Hence, the area of the plot is 4500 m²

Given that, width of the path = 2 m

Length $\sf = (75 - 2 \times 2) \ m = (75 - 4) \ m$

$\longrightarrow \sf 71 \ m$

Breadth = $\sf (60 - 2 \times 2) \ m = (60 - 4) \ m$

$\longrightarrow \sf 56 \ m$

Area of a rectangle = Length × Breadth

Substituting their values,

Area = $\sf 71 \times 56$

$\longrightarrow \sf 3976 \ m^{2}$

Hence, area of the rectangle is 3976 m²

Finding area of the path,

Area of the path = Area of the plot - Area of rectangle

Substituting them,

Area of the path = $\sf 4500 - 3976$

$\longrightarrow \sf 524 \ m^{2}$

Hence, area of the path is 524 m²

Given that, cost of constructing per meter is Rs. 125

Cost of constructing = Area of the path × Cost per meter

Substituting their values,

Cost of constructing = $\sf 524 \times 125$

$\longrightarrow \sf Rs. \ 65500$

Hence, the cost of constructing is Rs. 65500