Determining the Length and Breadth of 150 Square Meter Land

Understanding the relationship between length and breadth in a rectangular area is a fundamental concept in geometry and can be applied to various practical scenarios, such as land measurement and space planning. Given an area of 150 square meters (150 sqm), we can explore how to find the possible length and breadth combinations that satisfy the area formula. This article will provide a detailed explanation and examples to help you fully grasp this concept.

Understanding the Area Formula

The area of a rectangle is calculated using the formula:

Area Length × Breadth

Given an area of 150 sqm, we can express this as:

L × B 150

Where:

L Length B Breadth

Since we have only one equation, we can have various combinations of length and breadth that will result in an area of 150 sqm. This means that there are countless possibilities for the length and breadth of such a land area. Let's explore a few examples:

Example Combinations

Length 15 m, Breadth 10 m

15 m × 10 m 150 sqm

Length 30 m, Breadth 5 m

30 m × 5 m 150 sqm

Length 12 m, Breadth 12.5 m

12 m × 12.5 m 150 sqm

Length 150 m, Breadth 1 m

150 m × 1 m 150 sqm

From these examples, it is clear that as long as the product of the length and breadth equals 150 sqm, the area remains the same. If you have specific requirements, such as one dimension needing to be longer than the other, please let me know, and I will provide the suitable combinations.

Mathematical Explanation and Degrees of Freedom

Mathematically, to solve one equation, we need only one unknown. In the case of finding the length and breadth of a rectangle with a given area, we have one equation and one unknown at a time:

l × b A

Where:

l Length b Breadth A Area (150 sqm in this case)

However, since we are given only the area and not the specific length or breadth, we can plug any number in for l and get any number out for b, or vice versa. This is why there are literally infinite answers.

If you want to solve for both length and breadth, you need to specify either the length or the breadth, and verify that the area is indeed rectangular. With this additional information, we can use the formula:

l A / b or b A / l

Let's illustrate this with an example. Suppose you provide the breadth of 10 m, then the length would be:

l 150 sqm / 10 m 15 m

Similarly, if you provide the length of 15 m, then the breadth would be:

b 150 sqm / 15 m 10 m

Conclusion

While the concept of finding the length and breadth of a 150 sqm land area is straightforward, the multiple combinations demonstrate the importance of providing specific dimensions to achieve precise results. Understanding the area formula and the mathematical concept of degrees of freedom helps in accurately defining and solving geometric problems.