Calculate the total cost of constructing a path at ₹80/ $m 2$ and laying grass at ₹40/ $m 2$ and laying grass at ₹40/, if a rectangular plot of land measures $95 m × 72 m$ , if a rectangular plot of land measures and inside the plot, a path of uniform width of 3.5m is to be constructed all around while the rest is laid with grass.

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Detailed Solution

We know that area of a rectangle is

l e n g t h × b r e a d t h

.
First, we will find the area of the rectangular plot that is

95 m × 72 m

.
Area of the rectangular plot

= 6840 m 2

Now, we will find the area of the grassy plot, where the length of the plot

95 m − 2 × 3.5 m = 88 m

and the breadth of the plot is

72 m − 2 × 3.5 m = 65 m

.
So, the area of the grassy plot is

88 m × 65 m

.
Area of the grassy plot

= 5720 m 2

Further, we will find the area of the path which is equal to the area of the grass plot subtracted from the area of the rectangular plot.
Area of path

= 6840 m 2 − 5720 m 2

= 1120 m 2

We know that to find the total cost we will add the cost of laying grass on the plot and constructing the path on the plot.
Also, the cost of constructing a path is ₹80/