Let the length of the rectangle be $L$ cm. According to the problem, the width of the rectangle is one-third of the length, so we can express the width as $\frac{1}{3}L$ cm.

The formula for the perimeter of a rectangle is: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$ We are told that the perimeter is 48 cm. Substituting the values into the formula: $48 = 2 \times (L + \frac{1}{3}L)$ Simplify inside the parentheses: $48 = 2 \times \left( \frac{3}{3}L + \frac{1}{3}L \right)$ $48 = 2 \times \frac{4}{3}L$ Now, divide both sides by 2: $24 = \frac{4}{3}L$ To solve for $L$, multiply both sides by 3: $72 = 4L$ Now, divide both sides by 4: $L = 18 \, \text{cm}$

So, the length is 18 cm. To find the width, use the relationship $\text{Width} = \frac{1}{3}L$: $\text{Width} = \frac{1}{3} \times 18 = 6 \, \text{cm}$

Final Answer:

• Length = 18 cm
• Width = 6 cm

Let me know if you'd like more details or have any questions! Here are some related questions:

1. How does the formula for the perimeter of a rectangle change if we are dealing with a square?
2. What happens to the perimeter if the width is doubled?
3. How can we calculate the area of this rectangle?
4. If the perimeter was 72 cm instead of 48 cm, what would the new dimensions be?
5. How would the relationship between length and width change if the width were half the length instead?

Tip: When solving problems like these, always ensure that you're working with clear relationships between the variables before substituting into the formulas!