Find the cost of cultivating a rectangular field 34 m long and 18 m wide at Rs. 4.50 per sq. metre. Also, find the cost of fencing the field at Rs. 2.25 per metre.

Answer

To solve the problem step by step, we will calculate the area of the rectangular field, the cost of cultivating it, the perimeter for fencing, and finally the cost of fencing.

### Step 1: Calculate the Area of the Field
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Width} \]
Given:
- Length = 34 m
- Width = 18 m

Substituting the values:
\[ A = 34 \, \text{m} \times 18 \, \text{m} = 612 \, \text{m}^2 \]

### Step 2: Calculate the Cost of Cultivating the Field
The cost of cultivating the field is calculated by multiplying the area by the cost per square meter.
Given:
- Cost per square meter = Rs. 4.50

So, the cost of cultivation \( C_c \) is:
\[ C_c = \text{Area} \times \text{Cost per square meter} = 612 \, \text{m}^2 \times 4.50 \, \text{Rs/m}^2 \]
Calculating this:
\[ C_c = 612 \times 4.50 = 2754 \, \text{Rs} \]

### Step 3: Calculate the Perimeter of the Field
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
Substituting the values:
\[ P = 2 \times (34 \, \text{m} + 18 \, \text{m}) = 2 \times 52 \, \text{m} = 104 \, \text{m} \]

### Step 4: Calculate the Cost of Fencing the Field
The cost of fencing is calculated by multiplying the perimeter by the cost per meter.
Given:
- Cost per meter = Rs. 2.25

So, the cost of fencing \( C_f \) is:
\[ C_f = \text{Perimeter} \times \text{Cost per meter} = 104 \, \text{m} \times 2.25 \, \text{Rs/m} \]
Calculating this:
\[ C_f = 104 \times 2.25 = 234 \, \text{Rs} \]

### Final Answers:
- Cost of cultivating the field: Rs. 2754
- Cost of fencing the field: Rs. 234

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