A square plot of land has an area of 289 square feet. What will be the cost of building a fence around this square plot if the price per foot of fencing is Rs. 58?

Introduction / Context:This question requires converting area of a square into side length, then using that to compute the perimeter and finally the fencing cost. It brings together basic geometry and simple arithmetic cost calculation.

Given Data / Assumptions:- Area of square plot = 289 square feet.- Cost of fencing = Rs. 58 per running foot.- We assume fencing is required on all four sides of the square.

Concept / Approach:For a square, if the side length is s, then:Area = s^2Perimeter = 4 * sWe first find the side from the area, then the perimeter, and finally multiply the perimeter by the cost per foot to get the total cost of fencing.

Step-by-Step Solution:Step 1: Let side of square = s feet.Step 2: Given s^2 = 289.Step 3: Since 17 * 17 = 289, s = 17 feet.Step 4: Perimeter of the square = 4 * s = 4 * 17 = 68 feet.Step 5: Cost per foot = Rs. 58.Step 6: Total cost = 68 * 58 rupees.Step 7: Compute 68 * 58 = (68 * 60) - (68 * 2) = 4080 - 136 = 3944.

Verification / Alternative check:You can also multiply 58 * 68 directly in parts: 58 * 70 = 4060, then subtract 58 * 2 = 116 to get 4060 - 116 = 3944. Both methods confirm the same total cost.

Why Other Options Are Wrong:- 3748, 3847 and 3154 result from incorrect multiplication or from using the wrong side length or perimeter. None equals 68 * 58.

Common Pitfalls:- Taking the square root of 289 incorrectly, for example using 19 instead of 17.- Forgetting that fencing cost is based on perimeter, not area, and mistakenly multiplying area by cost per foot.

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