What will be the total cost of building a fence around a square plot whose area is 289 square feet, if the cost of fencing is Rs. 58 per foot?

Introduction / Context:
This problem is a blend of basic geometry and unit cost calculation. You are given the area of a square plot and the cost per foot to build a fence around it. The task is to find the total fencing cost, which requires first finding the perimeter of the square from its area and then multiplying by the cost per unit length.

Given Data / Assumptions:

The plot is a square with area 289 square feet.
The cost of building a fence is Rs. 58 per foot of fencing.
We need to find the total cost of fencing the entire boundary of the square plot.
All sides of the square are equal in length.

Concept / Approach:
For a square, area = side^2. From the given area, we find the side length by taking the square root. Once the side is known, the perimeter of the square is 4 times the side length. The total fencing cost is then perimeter multiplied by the cost per foot. Accuracy in computing the square root and multiplication is essential here.

Step-by-Step Solution:
Step 1: Find the side length of the square from its area. Area of square = side^2 = 289 square feet. So, side = square root of 289. 289 is 17^2, so side = 17 feet. Step 2: Compute the perimeter of the square. Perimeter of square = 4 * side = 4 * 17 = 68 feet. Step 3: Compute the total cost of fencing. Cost per foot = Rs. 58. Total cost = perimeter * cost per foot = 68 * 58. Compute 68 * 58 = 68 * (60 - 2) = 68 * 60 - 68 * 2 = 4080 - 136 = Rs. 3944.

Verification / Alternative Check:
We can quickly multiply in the standard way as well: 58 * 68. Doing the multiplication confirms the product 3944. Also, side 17 feet squared equals 289 square feet, which matches the given area, confirming that the side and perimeter values are correct and consistent with the problem statement.

Why Other Options Are Wrong:
Option Rs. 3748 would correspond to a different perimeter or cost per foot and does not result from 68 * 58.
Option Rs. 3847 is not a multiple of 58 and therefore cannot represent the correct result for a whole number of feet.
Option Rs. 3154 is significantly lower than the true cost and would come from an incorrect side length or perimeter calculation.

Common Pitfalls:
A common mistake is to miscalculate the square root of 289, sometimes confusing it with 19 or another nearby number. Others may incorrectly treat the given area as perimeter. Errors can also occur in the multiplication step if done too quickly. Carefully using area = side^2 and perimeter = 4 * side avoids these issues.

Final Answer:
The total cost of building the fence around the plot is Rs. 3944.