Solving for the Width of a Rectangle Given Its Area and Length

Imagine a rectangular area in a geometric problem where the area is given as 50 square meters (m2) and the length is stated as 100 meters (m). The task is to determine the width of the rectangle. This problem is a common application of basic arithmetic and algebra that can be approached using the fundamental formula associated with the area of a rectangle.

Area Formula for a Rectangle: A L x W

The area of any rectangle can be calculated by multiplying its length by its width. The formula is straightforward:

A L x W

In this problem, the area (A) is 50 m2 and the length (L) is 100 m. Our goal is to find the width (W). We can rearrange the formula to isolate the width:

W A / L

Substituting the given values:

A 50 m2 L 100 m

Calculation

Let's perform the calculation step by step:

Substitute the known values into the formula: W 50 m2 / 100 m W 1/2 m or 0.5 m

Therefore, the width of the rectangle is 0.5 meters (0.5 m).

Understanding and Applying the Concept

This problem not only helps in understanding the application of the area formula but also aids in reinforcing basic arithmetic skills. The concept of dividing the area by the length to find the width is fundamental in geometry, and mastering such problems enhances problem-solving abilities in mathematics.

Practical Applications

The ability to calculate the dimensions of a rectangle based on known measurements is useful in various real-world scenarios. For instance:

Construction and Building Design: Architects and builders use these calculations to ensure the placement of materials and structures fits within specified areas. Land Scaping: Landscape designers can use these calculations to plan the layout of properties accurately. Later Calculations: Knowing the dimensions of a rectangle allows for further calculations such as perimeter and volume.

By solving such problems, one can improve their mathematical prowess and gain a deeper understanding of geometric principles.

Conclusion

Understanding the relationship between the length and the width of a rectangle, given its area, is a crucial skill in geometry and its applications. The problem discussed here is a simple yet fundamental example that can be extended to more complex scenarios. Mastering these basics will serve as a solid foundation for tackling more advanced mathematical problems.