Question

The area of the square field is 1764 sq. m. How much will it cost to build a wall around it at a cost of Rs. 240 per metre?

Answer 1

Hint: Here we are given the area of a square field and we have to find the cost to build the wall around it i.e. they asked for the perimeter. So, first of all we will find the side of the square by the formula:
$ \Rightarrow A = {a^2}$, where A is the area of square and a is the side of square.
After this find the perimeter by putting value of side which is given by formula:
$ \Rightarrow P = 4 \times a$ where P is the perimeter of square.
If the cost of one metre wall is given then we can calculate the cost of the required wall by multiplying the perimeter with the cost.

Complete step-by-step answer:
We have given with the area of square field i.e.
$ \Rightarrow A = 1764{m^2}$
We can calculate the side of the square field i.e. a from the formula of area of square i.e. A
$ \Rightarrow A = {a^2}$
Put the value of A in this formula we get,
$ \Rightarrow {a^2} = 1764$
By taking square root of each side we get,
$ \Rightarrow a = \sqrt {1764} $
$ \Rightarrow a = 42m$ …….(1)
We can now calculate the perimeter i.e. P of the square field by the formula:
$ \Rightarrow P = 4 \times a$
Put the value of a from (1),
$ \Rightarrow P = 4 \times 42$
$ \Rightarrow P = 168m$
We have given that the cost of the wall per metre is Rs. 240. They have asked the cost of building a wall around it i.e. around the perimeter of the square field. So,
If cost of one metre $ = Rs.240$
Then the cost of 168 m wall$ = Rs.168 \times 240$
Therefore, the cost of 168 m wall$ = Rs.40,320$
Hence, the total cost of the wall is Rs. 40,320.
$ \Rightarrow a = 42$

Note: Some students do this question wrong they take area while calculating total cost for building the wall. But in this question, they asked for building the wall around the square field, which means around the boundaries. Perimeter gives the measure of the boundaries of figure while area gives the surface of the figure. If they asked for making a wooden floor then we will use the area while calculating the cost of the floor.