The cost of fencing a rectangular field at Rs. 7.50 per metre is Rs 600 .If its length is 24 m , find its breadth .

Options

A. 16 m
B. 16. 8 m
C. 20 m
D. 20 . 8m

Answer

To solve the problem step by step, we will follow the given information and apply the necessary formulas.

### Step 1: Understand the given information
We know the following:
- Cost of fencing per meter = Rs. 7.50
- Total cost of fencing = Rs. 600
- Length of the rectangular field (L) = 24 m

### Step 2: Calculate the perimeter of the rectangular field
The formula for the total cost of fencing is:
\[ \text{Total Cost} = \text{Cost per meter} \times \text{Perimeter} \]
Rearranging this formula to find the perimeter:
\[ \text{Perimeter} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]
Substituting the values:
\[ \text{Perimeter} = \frac{600}{7.50} \]

### Step 3: Perform the division
Calculating the perimeter:
\[ \text{Perimeter} = \frac{600}{7.50} = 80 \text{ meters} \]

### Step 4: Use the perimeter to find the breadth
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]
Where L is the length and B is the breadth. We can rearrange this to find the breadth:
\[ 80 = 2(24 + B) \]
Dividing both sides by 2:
\[ 40 = 24 + B \]

### Step 5: Solve for breadth (B)
Now, we can isolate B:
\[ B = 40 - 24 \]
\[ B = 16 \text{ meters} \]

### Final Answer
The breadth of the rectangular field is **16 meters**.

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