Introduction
Calculating the length of a rectangle when you know its area and width is a fundamental problem in geometry. By understanding the relationship between the area, width, and length of a rectangle, you can easily determine the missing dimension. This guide will take you through the process step-by-step, providing clear explanations and examples along the way.
Understanding the Relationship
The area \( A \) of a rectangle can be found by multiplying its length \( L \) by its width \( W \), expressed by the formula:
\[ A = L \times W \]
When the area \( A \) and the width \( W \) are known, you can rearrange this formula to solve for the length \( L \):
\[ L = \frac{A}{W} \]
This formula tells us that to find the length of a rectangle, we divide its area by its width.
Step-by-Step Calculation
Let's work through an example to illustrate the process.
Example:
Suppose we have a rectangle with an area of 24 square units and a width of 4 units. We want to find the length of the rectangle.
Step 1: Identify the Given Values
Given:
- Area \( A = 24 \) square units
- Width \( W = 4 \) units
Step 2: Use the Formula to Find the Length
Using the formula \( L = \frac{A}{W} \), substitute the given values:
\[ L = \frac{24}{4} \]
Step 3: Perform the Division
Now, calculate the length:
\[ L = 6 \]
Final Value
For a rectangle with an area of 24 square units and a width of 4 units, the length is 6 units.
