Question

rectangle of length 30 m and width 16 m.
10) The area of a square field is 49,284 m². Find
the cost of fencing the field at 15 per metre.​

Answer 1

Given :

• Area of square field = 49,284 m²

• Rate of fencing the field = Rs. 15

To find :

• Cost of fencing the field

Concept :

Fencing is always done to the boundaries. And perimeter is the sum of all the sides [Boundaries.] So, firstly we will calculate the side of the square field by using the formula of area of square. Then after getting its value we will calculate the perimeter and multiply he resultant value by the rate of fencing the field. The resultant value will be our required answer.

Formula of area of square :-

• Area of square = side²

Formula of perimeter of square :-

• Perimeter of square = 4 × side

Solution :

Calculating the side of the square field :-

⟶ Area of square = side²

⟶ 49,284 = side²

⟶ Taking square root on both the sides ::

⟶ √49,284 = side

⟶ √(222 × 222) = side

⟶ ± 222 = side

⟶ As we know, the side of the square cannot be negative. So, the negative sign will get rejected.

⟶ ± 222 Reject -ve = side

⟶ 222 = side

Therefore, the side of the square field = 222 m

Now, calculating the perimeter of the square :-

⟶ Perimeter of square field = 4 × 222

⟶ Perimeter of square field = 888

Therefore, the perimeter of the square field = 888 m

⟶ Cost of fencing the field = Perimeter of the square field × Rate of fencing

⟶ Cost of fencing the field = 888 × 15

⟶ Cost of fencing the field = 1332

Therefore,

• The cost of fencing the square field = Rs. 1332