Question

The area of the square field is 1763 sq m. How much will cost to build a wall around it at the cost of Rs.240 per meter?

Answer 1

Hint: At first using the formula for the area of a square we’ll find the measure of the side, then using the side of the field we’ll find the perimeter on which the wall is to be made.
Then using the rate of the wall and the perimeter we’ll find the total cost required for the wall.

Complete step-by-step answer:
Given data: Area of the square field is 1764 sq m
Rate of building the wall per metre is Rs.240

We know that area of a square$ = {(side)^2}$
Therefore the area of the square field$ = {(side)^2}$
$ \Rightarrow 1764 = {(side)^2}$
Taking square root on both sides, we get,
$ \Rightarrow side = 42$
Therefore, the side of the square field=42m
We know that the wall will be built at the perimeter of the square field
And the perimeter of a square is 4(side of the square)
Therefore, the perimeter of the square field is 4(side of the square field)
The perimeter of the square field\[ = 4\left( {42} \right)\]

\[ = 168{\text{ }}m\]
Now,the total cost of building the wall $ = $rate of building the wall$ \times $ perimeter of square field
As, Rate of building the wall per metre is Rs.240
And perimeter of square field is 168m
On substituting the values in above equation, we get,
\[ \Rightarrow \] The total cost of building the wall $ = 240 \times 168$
\[ \Rightarrow \] The total cost of building the wall $ = 40320$
Therefore, the total cost of building the wall is Rs.40320.
Note: During the multiplication of the rate and the perimeter always check the unit of measurements like if the rate is in rupees per meter and the perimeter is in centimeter then we should always convert both into similar or like terms. We can do this either by converting rate into rupees per centimeter or by converting perimeter into meters.