Area Calculation of a Rectangle Using Perimeter and Length-Breadth Relationship

Determining the area of a rectangle when given specific conditions can be a fascinating exercise in algebraic problem-solving. This article walks you through the process step by step, using real problems to illustrate the method.

Understanding the Problem

The problem at hand involves a rectangle where the difference between its length and breadth is 20 meters, and its perimeter is 100 meters. Our goal is to find the area of this rectangle. To achieve this, we will use algebra to solve for the dimensions and then calculate the area.

Solving the Problem

Let's denote:

1. Length of the rectangle as l

2. Breadth of the rectangle as b

We have two key pieces of information:

The difference between the length and breadth is 20 meters. The perimeter of the rectangle is 100 meters.

Mathematically, these can be expressed as:

l - b 20 2l 2b 100, which simplifies to l b 50

Now, let's solve these equations simultaneously:

Step 1: Eliminating b

Add the two equations:

l - b l b 20 50

This simplifies to:

2l 70

Solving for l, we get:

l 35 meters

Step 2: Finding b

Substitute l 35 into one of the original equations:

35 b 50

Solving for b, we get:

b 15 meters

Step 3: Calculating the Area

Now that we have the length and breadth, we can calculate the area:

Area l × b 35 × 15

Area 525 square meters

Alternative Methods for Similar Problems

To further illustrate the process, let's consider a similar problem with different values:

Problem: If the width (breadth) equals x and the length equals x - 20, and the perimeter is 100 meters:

Using the perimeter equation:

2(x x - 20) 100

2(2x - 20) 100

4x - 40 100

4x 140

x 35 meters

Length x - 20 35 - 20 15 meters

Area 35 × 15 525 square meters

Conclusion

The area of a rectangle can be calculated when given specific conditions such as the difference between length and breadth, and the perimeter. By solving the equations, we can determine the dimensions and then compute the area. This method is not only useful for mathematical problems but also for real-world applications in design and construction.

For further reading on related topics, consider exploring:

Perimeter of a Rectangle Length and Breadth Relationship Rectangle Area Calculation