To solve this, we can follow these steps:

Step 1: Define the variables

Let the width of the rectangle be $w$.
Then the length of the rectangle is $4w$.
The formula for the perimeter of a rectangle is: $P = 2 \times (\text{length} + \text{width})$ Substitute the given values: $120 = 2 \times (4w + w)$

Step 2: Simplify the equation

$120 = 2 \times 5w$ $120 = 10w$ $w = \frac{120}{10} = 12$

Step 3: Find the length

The length is: $4w = 4 \times 12 = 48$

Step 4: Calculate the area

The area of a rectangle is: $\text{Area} = \text{length} \times \text{width}$ $\text{Area} = 48 \times 12 = 576$

Final Answer:

The area of the rectangle is 576 square units.

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Would you like a detailed explanation of any specific step? Here are some related questions to consider:

1. What if the width was tripled instead of quadrupled?
2. How does the formula for the perimeter differ for other shapes?
3. Can we verify the solution with another method?
4. What is the ratio of length to width in this rectangle?
5. How does increasing the width affect the area while keeping the perimeter constant?

Tip: Always double-check your work by substituting back into the original equations to verify correctness.