Calculating the Length of Wire Required to Fence a Rectangular Garden

When it comes to landscaping and construction projects, understanding the length of wire needed to fence a rectangular garden is a foundational concept. This article will break down the process of calculating the perimeter and subsequently the total length of wire required to fence a garden, four times over.

Understanding the Given Information

A rectangular garden is described with a perimeter of 60 meters and a length of 10 meters. The perimeter of a rectangle is given by the formula:

Perimeter 2(length width)

Given:

To find the width (W), we use the perimeter formula:

60 2(L W)

Rearranging to solve for W:

60 2(10 W)

30 10 W

W 20 meters

Determining the Length of Wire Required

The question asks for the length of wire required to fence the garden four times over. The first step is to find the perimeter of the garden:

Perimeter 60 meters

Since the perimeter is the total length of wire required to fence the garden once, for four times, the length of wire required is:

Length of wire required 4 × 60 meters 240 meters

Exploring Different Approaches

Let's explore an alternative approach using algebraic expressions:

Given the perimeter (P) and length (L) of the rectangle:

P 60 meters

L 10 meters

To find the width (W), we can use the perimeter formula:

2L 2W 60

2W 60 - 2L

2W 60 - 20

2W 40

W 20 meters

Now, to find the length of wire required to fence the garden four times:

Length of wire required 4 × (2L 2W) 4 × 60 meters 240 meters

Mathematical Verification

For verification, we can use a step-by-step approach:

Perimeter 2 × Length 2 × Width

60 2 × 10 2 × Width

60 20 2 × Width

40 2 × Width

Width 20 meters

Thus, the dimensions of the garden are 10 meters by 20 meters.

The length of wire required to fence the garden four times is:

Length of wire required 4 × (10 20) 4 × 30 120 meters, but since we need to fence the perimeter four times:

Length of wire required 4 × 60 240 meters

Conclusion

In conclusion, the length of wire required to fence a rectangular garden, given its perimeter and length, and to fence it four times, is 240 meters. This calculation is crucial for any landscaping or construction project, ensuring that the necessary materials are available and budget is managed accordingly.