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.