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------------------------------------------------ The length of a rectangle is 4 times the width. The perimeter is 120 cm.

Find the dimensions of the rectangle.

To solve the problem of finding the dimensions of the rectangle, follow these steps:

1. Understand the Relationship: We know the length of the rectangle is 4 times the width. Let's call the width of the rectangle "w" cm. Therefore, the length would be "4w" cm.

2. Use the Perimeter Formula: The formula for the perimeter [tex]\(P\)[/tex] of a rectangle is:
[tex]\[
P = 2 \times (\text{length} + \text{width})
\][/tex]
We're given that the perimeter is 120 cm. So, we can set up the equation:
[tex]\[
2 \times (4w + w) = 120
\][/tex]

3. Simplify the Equation: Simplify the expression inside the parentheses:
[tex]\[
2 \times (5w) = 120
\][/tex]
This simplifies to:
[tex]\[
10w = 120
\][/tex]

4. Solve for the Width: Divide both sides of the equation by 10 to find the width:
[tex]\[
w = \frac{120}{10} = 12
\][/tex]
So, the width of the rectangle is 12 cm.

5. Find the Length: Since the length is 4 times the width, calculate the length:
[tex]\[
\text{Length} = 4 \times 12 = 48 \text{ cm}
\][/tex]

Therefore, the dimensions of the rectangle are a width of 12 cm and a length of 48 cm.