Solving the Rectangle Width: A Practical Guide Using Ratios

When dealing with geometric shapes, understanding the relationships between their dimensions is crucial. This article provides a step-by-step guide on how to calculate the width of a rectangle given its length and the ratio of its length to its width. Specifically, we will solve the problem where the ratio of the length to the width of a rectangle is 4:3, and the length is 84 cm.

Understanding the Ratio

A ratio of 4:3 means that for every 4 units of length, there are 3 units of width. This relationship can be written as:

Length : Width 4 : 3

Step-by-Step Solution

To find the width, let's define the variables first:

The given ratio can be expressed as a fraction:

Length / Width 4 / 3

Substituting the known length into the equation:

84 / W 4 / 3

Cross-Multiplication Technique

Using cross-multiplication to solve for W:

4W 3 x 84

4W 252

Dividing both sides by 4 to find W:

W 252 / 4

W 63 cm

Thus, the width of the rectangle is 63 cm.

Alternative Solutions

There are several ways to solve the same problem. Here are a few alternative methods:

Multiplication and Division Technique

Algebraic Approach

Relatable Explanations

This problem is a classic example used in middle school and high school math to demonstrate the application of ratios in real-world scenarios. It helps students understand how to use algebraic methods to solve geometric problems. The problem also involves basic arithmetic operations and the manipulation of equations.

Conclusion

Using the given ratio and some simple math, we can determine the width of a rectangle. This approach not only helps in solving mathematical problems but also in understanding the concept of ratios and proportions in practical scenarios.