Question

The area of a square field is 65536 $ m^2 $ . Find the cost of fencing it at the rate of Rs. 5 per metre.

Answer 1

Hint: We have given the area of a square field and the rate of fencing per metre. To find the total cost, firstly we have to calculate the side of the square field. This can be calculated with help of the area of the field. After calculating the side we have to calculate the perimeter of the field. This perimeter helps us in calculating the cost of fencing the square field.

Complete step-by-step answer:
We have given that; Area of square field = 65536 $ m^2 $
Area of the square is equal to = side× side
Let ‘a’ be the side of the square, then $ a \times a = 65536 $
 $ {a^2} = 65536 $
 $ a = \sqrt {65536} $
 $ a = 256 $ so, side of the square = 256 m
Now, we have to calculate the perimeter of the square. Perimeter of the square is the length of all the boundaries of the square. Since, there are 4 sides of square of equal length therefore ;
Perimeter of square = $ 4 \times side $
Side of square = 256 m
So, perimeter of square $ = 4 \times 256 = 1024 $
Perimeter of square is 1024 m
Now we can calculate the cost of fencing the field. We have given that the cost of fencing of 1m is 5Rs.
So, cost of fencing the boundaries = perimeter × 5
 $ = 1024 \times 5 = 5120 $
Therefore the total cost of fencing is 5120 Rs.
So, the correct answer is “5120 RS”.

Note: Area of square is defined as the number of square units needed to fill a square. In general Area is defined as the region occupied inside the boundary of the flat object or figure.
Perimeter The perimeter of any closed geometrical object is defined as the distance around the object. For square the perimeter is calculated by adding its all four sides