To calculate the cost of fencing the property, we first need to determine the perimeter of the rectangular property and then multiply it by the cost per meter of fencing.

Step 1: Find the width of the rectangular property

We are given:

• The area of the property is 5 km².
• The length is 10 km.

The area of a rectangle is given by the formula: $\text{Area} = \text{Length} \times \text{Width}$

Substitute the given values: $5 = 10 \times \text{Width}$

Solving for the width: $\text{Width} = \frac{5}{10} = 0.5 \, \text{km}$

So, the width of the property is 0.5 km.

Step 2: Calculate the perimeter of the property

The perimeter $P$ of a rectangle is given by: $P = 2 \times (\text{Length} + \text{Width})$

Substitute the values: $P = 2 \times (10 + 0.5) = 2 \times 10.5 = 21 \, \text{km}$

Step 3: Convert the perimeter to meters

Since 1 km = 1000 meters, the perimeter in meters is: $21 \, \text{km} = 21 \times 1000 = 21,000 \, \text{meters}$

Step 4: Calculate the total cost of fencing

The cost of fencing is $3.1 per meter. Therefore, the total cost is: $\text{Total cost} = 21,000 \times 3.1 = 65,100 \, \text{dollars}$

Final Answer:

The total cost to fence the property is $65,100.

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Would you like a more detailed explanation or help with another question?

Here are some related questions:

1. How would the cost change if the property was a square instead of a rectangle?
2. What would the area and perimeter be if the width was doubled?
3. How would the cost of fencing change if the price per meter increased to $4.50?
4. What other factors could affect the cost of fencing a property besides price per meter?
5. If the property were to be fenced with different types of materials, how might that affect the cost?

Tip: It's always helpful to first break down the problem into smaller parts, such as finding the width from the area and using the correct formula for perimeter before calculating costs.