Find the cost of fencing a rectangular park of length 250 m and breadth 175 m at the rate of Rs. 12 per metre

Question

Accepted Answer

To determine the cost of fencing a rectangular park, we first need to calculate the perimeter of the park. The formula for the perimeter $ P $ of a rectangle is given by:

$$ P = 2 \times (\text{Length} + \text{Breadth}) $$

Given:
- Length = 250 meters
- Breadth = 175 meters

Substituting these values into the formula, we get:

$$ P = 2 \times (250 + 175) $$
$$ P = 2 \times 425 $$
$$ P = 850 \text{ meters} $$

The cost of fencing is given at the rate of Rs. 12 per meter. Therefore, the total cost $ C $ of fencing the park is calculated by multiplying the perimeter by the cost per meter:

$$ C = 850 \times 12 $$
$$ C = 10,200 \text{ Rs.} $$

Thus, the cost of fencing the park is Rs. 10,200, which corresponds to Option 2.

**Explanation for why each option is incorrect:**

1. **Option 1: Rs. 5100** - This option is incorrect because it underestimates the cost. The calculation of the perimeter and the rate per meter clearly shows that the total cost is Rs. 10,200, not Rs. 5100.

2. **Option 3: Rs. 3000** - This option is incorrect as it significantly underestimates the cost. The perimeter calculation and the rate per meter confirm that the cost is Rs. 10,200, not Rs. 3000.

3. **Option 4: Rs. 4200** - This option is incorrect because it also underestimates the cost. The correct calculation of the perimeter and the rate per meter results in a total cost of Rs. 10,200, not Rs. 4200.

In conclusion, the correct answer is Option 2: Rs. 10,200, as it accurately reflects the cost of fencing the park based on the given dimensions and rate.