The cost of fencing a rectangular field at Rs. 8.50 per metre is Rs. 850. If its length is 32 m, find its breadth.

Options

A. 18 m
B. 10 m
C. 8 m
D. 12 m

Answer

To solve the problem, we need to find the breadth of a rectangular field given the cost of fencing and the length. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We know the cost of fencing a rectangular field is Rs. 850, and the cost per meter is Rs. 8.50. The length of the field is given as 32 meters. We need to find the breadth of the field.

### Step 2: Calculate the Total Perimeter
First, we need to find the total length of fencing (perimeter) that was done.

The formula for the cost of fencing is:
\[ \text{Total Cost} = \text{Cost per meter} \times \text{Perimeter} \]
Substituting the known values:
\[ 850 = 8.50 \times \text{Perimeter} \]

### Step 3: Solve for Perimeter
To find the perimeter, we can rearrange the equation:
\[ \text{Perimeter} = \frac{850}{8.50} \]
Calculating this gives:
\[ \text{Perimeter} = 100 \text{ meters} \]

### Step 4: Use the Perimeter Formula for a Rectangle
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the known values:
\[ 100 = 2 \times (32 + \text{Breadth}) \]

### Step 5: Simplify the Equation
Dividing both sides by 2:
\[ 50 = 32 + \text{Breadth} \]

### Step 6: Solve for Breadth
Now, we can isolate the breadth:
\[ \text{Breadth} = 50 - 32 \]
Calculating this gives:
\[ \text{Breadth} = 18 \text{ meters} \]

### Conclusion
The breadth of the rectangular field is 18 meters.

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