Introduction

The perimeter and dimensions of a rectangle are essential in various mathematical and real-world applications. This article will guide you through the process of finding the width of a rectangle given the length and the perimeter using different methods. We will explore multiple techniques and solutions to ensure a comprehensive understanding.

Rectangular Geometry and Perimeter Formula

A rectangle is a quadrilateral with four right angles. The perimeter (P) of a rectangle is the total distance around its boundary and is given by:

P 2l 2w

Where:

l is the length of the rectangle w is the width of the rectangle

The Problem: Given Length and Perimeter

Often, we are given the length (l) as being three times the width (w), and the perimeter (P). This problem asks us to find the width (w).

Method 1: Ratio and Division

Let's start by defining the variables:

Width w cm Length 3w cm since the length is three times the width

Given:

Perimeter (P) 36 cm

Using the perimeter formula:

P 2(3w) 2w

36 6w 2w

36 8w

Divide both sides by 8:

W 36 / 8 4.5 cm

Method 2: Combined Perimeter Formula

Another way to write the perimeter formula with the given relationship is:

36 2(3w) 2w

36 6w 2w

36 8w

Again, divide both sides by 8:

W 36 / 8 4.5 cm

Method 3: Simplified Ratio Approach

We can also divide the total perimeter by 4 (since the ratio of length to width is 3:1, making four parts in total).

Divide 36 cm into 4 parts:

Width 1 part 36 / 4 9 cm

Length 3 parts 9 x 3 27 cm

Conclusion

Through various methods and applications, we have successfully determined that the width of the rectangle is 4.5 cm when the length is three times the width and the perimeter is 36 cm.

Related Keywords

rectangle perimeter width calculation length calculation perimeter formula