Question

The cost of cultivating a square field is Rs. 130/- per meter is Rs. 8450/-. Find the length of each
side of the field.​

Answer 1

Given :

• Rate of cultivating the sqaure field = Rs. 130
• Total cost of cultivating the sqaure field = Rs. 8450

To find :

• Length of the each side of the field

Concept :

To find the length of each side of the field :-

• Firstly calculate the area of the field.
• For finding the area, divide the total cost of cultivating the field by the rate of cultivating the field. The resultant value will be the area of the field.
• Then by using the formula of area of square find the side of the field.

Formula of area of square :-

• Area of square = side × side

Solution :

Area of the square field :-

➪ Area of the square field = Total cost of cultivating the field ÷ Rate of cultivating the field

Substituting the given values, we get :-

➪ Area of the square field = 8450 ÷ 130

➪ Cancelling the zeroes.

➪ Area of the sqaure field = 845 ÷ 13

➪ Area of the square field = 65

∴ Area of the square field = 65 m²

Using formula,

★ Area of the sqaure field = side × side

Substituting the given values, we get :-

➪ 65 = side²

➪ Taking square root on both the sides.

➪ √65 = side

➪ ± 8.06 = side

➪ As we know, side of the square cannot be in negative, so the negative sign will get cancelled.

➪ ± 8.06 Reject - ve = side

➪ 8.06 = side

★ Side of the square = 8.06 m

Therefore,

• Length of each side of the square field = 8.06 m

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Let's verify our answer!!

To verify the answer, firstly we will calculate the area of the sqaure field and then multiply the area by the rate of cultivating the field. If the total cost will be equal to Rs. 8450 (as mentioned in the question) then the value of length of each side is correct.

➪ Area of sqaure field = side²

➪ Area of sqaure field = (8.06)²

➪ Area of sqaure field = 64.96

➪ On rounding off,

➪ Area of square field = 65

∴ Area of the square field = 65 m²

Now, we will find the total cost of cultivating.

Multiplying the area by the rate :-

➪ Total costing = 65 × 130

➪ Total cost = 8450

∴ Total costing of cultivating the field = Rs. 8450

Hence, verified.