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We are tasked with finding the width of a rectangle where the length is four times the width, and the area of the rectangle is 1024 cm².

### Let's define the variables:
- Let the width of the rectangle be \( w \) cm.
- Since the length is four times the width, the length of the rectangle will be \( 4w \) cm.
- The area \( A \) of a rectangle is given by the formula:
  \[
  A = \text{length} \times \text{width}
  \]

### Substituting the given values:
\[
1024 = w \times 4w
\]
\[
1024 = 4w^2
\]

### Solving for \( w \):
1. Divide both sides by 4:
   \[
   w^2 = \frac{1024}{4} = 256
   \]
2. Take the square root of both sides:
   \[
   w = \sqrt{256} = 16
   \]

Thus, the width of the rectangle is **16 cm**.

Would you like further details or clarifications?

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Here are five related questions to deepen your understanding:
1. How would you calculate the length of the rectangle now that you know the width?
2. If the area was doubled, what would be the new width?
3. What would happen to the width if the length was only three times the width?
4. How do you find the perimeter of the rectangle given the width and length?
5. Can the area of a rectangle ever be negative? Why or why not?

**Tip**: Always double-check your equation setup based on the problem conditions to avoid mistakes when solving geometric problems.

The length of a rectangle is four times its width. The rectangle has an area of 1024 cm². Work out the width of the rectangle.

Learn how to determine the width of a rectangle when the length is four times its width and the area is 1024 cm². This step-by-step solution includes key algebraic and geometric concepts, suitable for Grades 6-8 students.

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