Calculation and Understanding of Area and Dimensions for Rectangular Plots of Land

When dealing with the measurement of plots of land, understanding how to calculate the dimensions from the area can be crucial. In this article, we will explore how to find the breadth and perimeter of a rectangular plot whose area is given as 440 square meters. We will also discuss the various possible dimensions that could result in this particular area.

Determining the Breadth from the Area and Length

The area of a rectangular plot can be described using the formula for the area of a rectangle, which is Area Length × Breadth. Given that the area is 440 square meters (denoted as m2) and the length is 22 meters, we can calculate the breadth as follows:

Step 1: Use the area formula to find the breadth.

Breadth Area ÷ Length

Step 2: Plug in the given values.

Breadth 440 m2 ÷ 22 m

Step 3: Perform the division.

Breadth 20 m

Understanding the Perimeter of the Rectangular Plot

With the breadth known, we can also calculate the perimeter of the plot. The perimeter (P) of a rectangle is given by the formula:

P 2 × (Length Breadth)

Substituting the values we have:

Step 1: Plug in the length and breadth values.

P 2 × (22 m 20 m)

Step 2: Perform the addition inside the parentheses.

P 2 × 42 m

Step 3: Multiply by 2.

P 84 m

Thus, the perimeter of the rectangular plot is 84 meters.

Exploring Multiple Possible Dimensions

The given area of 440 square meters can be achieved through different dimensions, as long as the product of length and breadth equals 440. Let's explore some of these combinations:

1. 1 m × 440 m

2. 2 m × 220 m

3. 4 m × 110 m

4. 5 m × 88 m

5. 8 m × 55 m

6. 10 m × 44 m

7. 11 m × 40 m

8. 20 m × 22 m

Each of these combinations results in the same area of 440 square meters, demonstrating the versatility of rectangular plots with the same area but different dimensions. The smallest possible breadth is 1 meter while the largest is 22 meters in the example where length and breadth are in integer values.

Note on Fractional Dimensions

It's important to note that only integer values provide a perfect solution. If fractional dimensions are considered, the nearest perfect square to 440 m2 is 441 m2, which corresponds to 21 meters on each side (21 × 21 441). Any fractional combination would not yield exactly 440 m2, as the exact integer factors are the ones that provide the correct area.

In conclusion, understanding the relationship between the area and dimensions of a rectangular plot can be crucial in various applications, from landscaping to land surveying.