Finding the Breadth of a Rectangle Given Its Area and Length

Understanding the relationship between the area, length, and breadth of a rectangle is a fundamental concept in geometry. In this article, we will walk through how to calculate the breadth of a rectangle when the area and length are known. This knowledge is essential for various applications in construction, design, and real-world problem solving. Let's delve into the solution step by step.

Step-by-Step Solution

The formula to find the area of a rectangle is:

Area Length × Breadth

Given the area is 600 square centimeters (cm2) and the length is 30 centimeters (cm), we need to determine the breadth (b). The formula can be rearranged to solve for the breadth:

Breadth (b) Area / Length

Breadth (b) 600 cm2 / 30 cm 20 cm

Reiteration of the Solution

To summarize the solution, let's restate the problem in a structured form:

Problem statement:
Area of the rectangle 600 sq. cm
Length of the rectangle 30 cm

Step 1: Write the formula for the area of a rectangle:
Area Length × Breadth

Step 2: Substitute the given values into the formula:
600 30 × Breath

Step 3: Solve for the breadth by dividing both sides by the length:
Breadth 600 / 30 20 cm

Proof by Transformation

To further confirm the solution, consider another method: transforming the given information and solving the equation:

600 30 × Breadth

Divide both sides by 30 cm:

Breadth 600 / 30 20 cm

This reaffirms that the breadth is indeed 20 cm.

Real-world Application

Knowing how to calculate the breadth of a rectangle is useful in many practical scenarios, such as:

Designing rooms and other spaces in construction projects. Calculating the dimensions required for fabric or carpet in interior decoration. Solving layout and design problems in manufacturing.

Understanding and applying geometric formulas can help in making accurate and reliable measurements, leading to better and more efficient use of space and resources.

Conclusion

By following the steps outlined in this article, you can easily calculate the breadth of a rectangle when given its area and length. This skill is not only useful in academic settings but also in real-world applications. Practicing similar problems will enhance your understanding and improve your problem-solving abilities in geometry.