Solving for the Dimensions of a Rectangle Given its Perimeter and Length

Solving for the Dimensions of a Rectangle Given its Perimeter and Length

Introduction

When dealing with geometric shapes, understanding the relationship between different dimensions, such as the length and the breadth of a rectangle, is a fundamental concept. This article will walk you through the process of determining the length and breadth of a rectangle given its perimeter and a specific relationship between its length and breadth. We will explore multiple methods and solutions to arrive at the answer, ensuring clarity and a comprehensive understanding of the concept.

Problem Statement

A rectangle has a length that is 6 cm more than its breadth. If the perimeter of the rectangle is 80 cm, what are its length and breadth?

Method 1: Using Algebraic Equations

Let the breadth of the rectangle be x cm. Therefore, the length of the rectangle is x 6 cm.

The perimeter of a rectangle is given by the formula P 2(L B). Substituting the given values, we get:

P 2(x 6 x) 80

Simplifying the equation, we get:

2(2x 6) 80

Dividing both sides by 2:

2x 6 40

Now, solving for x:

2x 40 - 6

2x 34

x 17

Hence, the breadth of the rectangle is 17 cm. The length is:

x 6 17 6 23 cm

Method 2: Simplified Approach

Let the length of the rectangle be L and the breadth be B:

Given: L B 6 and P 2(L B) 80 cm.

Substituting L B 6 into the perimeter formula:

80 2[(B 6) B]

80 2(2B 6)

40 2B 6

34 2B

B 17 cm

Hence, the length L 17 6 23 cm

Verification and Additional Calculations

To verify the solution, we can calculate the perimeter:

P 2(23 17) 2(40) 80 cm

This confirms our solution is correct.

Summary

In this article, we explored multiple methods to determine the dimensions of a rectangle given its perimeter and the relationship between its length and breadth. The problem involved using algebraic equations and a simplified approach. We have provided detailed steps for each method and verified our solution.

Keywords

Perimeter, Length, Breadth