Problem:
A rectangular grassy land measuring 40 m by 25 m is to be surrounded externally by a path which is 2 m wide. Calculate the cost of leveling the path at the rate of Rs 8.25 per square meter.

Solution:

Step 1: Calculate the area of the grassy land:
The grassy land is in the shape of a rectangle, so we can use the formula for the area of a rectangle to find its area. The formula is given by:
Area = length × width
Given that the length of the grassy land is 40 m and the width is 25 m, we can substitute these values into the formula to find the area:
Area = 40 m × 25 m = 1000 square meters

Step 2: Calculate the area of the path:
To calculate the area of the path, we need to subtract the area of the grassy land from the area of the whole rectangular region including the path. The dimensions of the whole rectangular region including the path can be found by adding twice the width of the path to the length and width of the grassy land. Let's calculate the dimensions first:
Length of the whole rectangular region = length of the grassy land + 2 × width of the path
= 40 m + 2 × 2 m
= 40 m + 4 m
= 44 m

Width of the whole rectangular region = width of the grassy land + 2 × width of the path
= 25 m + 2 × 2 m
= 25 m + 4 m
= 29 m

Now, let's calculate the area of the whole rectangular region including the path using the formula:
Area = length × width
= 44 m × 29 m
= 1276 square meters

To calculate the area of the path, we subtract the area of the grassy land from the area of the whole rectangular region including the path:
Area of the path = Area of the whole rectangular region - Area of the grassy land
= 1276 square meters - 1000 square meters
= 276 square meters

Step 3: Calculate the cost of leveling the path:
The cost of leveling the path is given as Rs 8.25 per square meter. To calculate the cost, we multiply the area of the path by the cost per square meter:
Cost = Area of the path × Cost per square meter
= 276 square meters × Rs 8.25
= Rs 2277

Final Answer:
The cost of leveling the path at the rate of Rs 8.25 per square meter is Rs 2277.

Length -40 m
breadth-25m. it is the dimensions of grassy land

are of Grass land=25*40- 1000



then , length of excluding the land - 40+2+2-44

breadth of excluding the land=25+2+2- 29

Area of excluding the land=44*29- 1276m. sq..


area of. path= 1276-1000--276m. sq...

areof path. 276m. sq..



cost of leveling. 8.25 m. sq..

then,. cost of leveling 276. m sq..

276 *8.25----$2277.

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