Express the perimeter P of a rectangle as a function of the width W if the width of the rectangle is twice its length

To express the perimeter \( P \) of a rectangle as a function of its width \( W \), given that the width is twice its length, follow these steps:

### Step 1: Define the relationship between width and length.
Let \( L \) be the length of the rectangle. According to the problem, the width \( W \) is twice the length \( L \). So,
\[
W = 2L
\]
### Step 2: Express the length \( L \) in terms of the width \( W \).
From the equation \( W = 2L \), we can solve for \( L \) as follows:
\[
L = \frac{W}{2}
\]

### Step 3: Write the formula for the perimeter \( P \) of the rectangle.
The perimeter of a rectangle is given by:
\[
P = 2L + 2W
\]

### Step 4: Substitute the expression for \( L \) into the perimeter formula.
Substitute \( L = \frac{W}{2} \) into the perimeter formula:
\[
P = 2\left(\frac{W}{2}\right) + 2W
\]
Simplify this expression:
\[
P = W + 2W = 3W
\]

### Final Answer:
The perimeter \( P \) of the rectangle as a function of its width \( W \) is:
\[
P(W) = 3W
\]

Would you like further details or have any questions?

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Here are 5 related questions you might explore:
1. How would the perimeter function change if the width were three times the length?
2. What is the area of the rectangle as a function of its width \( W \)?
3. How does the perimeter function change if both the width and length are doubled?
4. How would you express the length as a function of the perimeter?
5. What happens to the perimeter if the width is halved?

**Tip:** When dealing with geometric problems, always try to express all quantities in terms of a single variable to simplify your calculations.

Learn how to express the perimeter P of a rectangle as a function of its width W. Follow a step-by-step solution where the width is twice the length. Suitable for students in Grades 7-9, covering geometric concepts and perimeter formulas.

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