Question

A rectangular grassy plot is $ 56\;m $ and $ 39\;m $ broad. It has a gravel path $ 2.5\;m $ wide all around it along its side. Find the area of the path and the cost of constructing it at $ Rs.4.50 $ per square metre.

Answer 1

Hint: Calculate the area of the total rectangular plot and then find the area of the rectangular grassy plot excluding the gravel path from all the sides and then find the area of the gravel path and also the cost in constructing it.

Complete step-by-step answer:
A rectangular grassy plot is $ 56\;m $ and $ 39\;m $ broad. It has a gravel path $ 2.5\;m $ wide all around it along its side. The cost of constructing is $ Rs.4.50 $ per square metre.
The diagram for the fields is shown below:

The area of the rectangular plot is equal to the product of length with breadth. So, the area of the total rectangular plot is equal to
 $ 56\;m \times 39\;m = 2184\;{m^2} $ .
Now take out the length and breadth of the gravel path. So, the length of the grassy plot becomes $ 56\;m - 2.5\;m - 2.5\;m = 51\;m $ and the breadth of the grassy plot becomes $ 39\;m - 2.5\;m - 2.5\;m = 34\;m $.
The area of the grassy plot only is equal to
 $ 51\;m \times 34\;m = 1734\;{m^2} $.
The area of the gravel path is equal to the subtraction of the total area and the area of grassy plot. So, the area of the gravel path is equal to
 $ 2184\;{m^2} - 1734\;{m^2} = 450\;{m^2} $ .
The cost of constructing the path is $ Rs.4.5 $ per metre square. So, the cost for constructing the gravel path is equal to
 $ 4.5 \times 450 = 2025 $ .
So, the cost for constructing the gravel path is equal to $ Rs.2025 $ .
So, the correct answer is “ $ Rs.2025 $ ”.

Note: The area of the gravel path is included in the total area with given dimensions and the rate is also given for gravel path only. So first calculate the area of the gravel path and then multiply it by the cost.