How to Calculate the Perimeter of a Rectangle Given Its Area and Breadth

Understanding the relationship between the area, length, and breadth of a rectangle is fundamental in geometry. In this article, we will walk through the process of calculating the perimeter of a rectangle when given its area and breadth.

Introduction

A rectangle is a quadrilateral with four right angles. The area of a rectangle is calculated by multiplying its length by its breadth. The perimeter, on the other hand, is the sum of all the sides of the rectangle. By knowing the area and the breadth, we can find the length and subsequently the perimeter. This article will demonstrate how to perform these calculations step by step.

Understanding the Formulae

The formulas we need to understand are:

Area of a rectangle: A Length × Breadth Perimeter of a rectangle: P 2(Length Breadth)

These formulae will be our primary tools in solving the problem at hand.

Problem Statement

A rectangle has an area of 28 cm2. If its breadth is 4 cm, find its perimeter.

Solution

First, let's use the area formula to find the length of the rectangle:

Area Length × Breadth

28 cm2 Length × 4 cm

Length 28 cm2 ÷ 4 cm 7 cm

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

Perimeter 2(Length Breadth)

Perimeter 2(7 cm 4 cm) 2 × 11 cm 22 cm

Verification

Let's verify our solution using the same steps:

A L × B 28 L × 4 4L 28 L 7 cm

P 2(L B) P 2(7 cm 4 cm) 2 × 11 cm 22 cm

Conclusion

By applying the formulas for the area and perimeter of a rectangle, we can solve a variety of geometric problems. In this example, we found that the perimeter of a rectangle with an area of 28 cm2 and a breadth of 4 cm is 22 cm. This method can be applied to any similar problem where the area and one dimension of a rectangle are known.

Additional Resources for Learning

For more detailed exploration and practice on the concepts discussed, you can refer to the following resources:

Math is Fun: Area and Perimeter - A comprehensive guide to understanding area and perimeter formulas. Khan Academy: Geometry - Area and Perimeter - Interactive lessons and practice problems to reinforce your learning.