The Formula { P = 2l + 2w $}$ Means That The Perimeter Of A Rectangle Is Equal To Twice The Sum Of Its Length And Its Width.Solve { P = 2l + 2w $}$ For { W $}$.A. { W = P - 2 - L $} B . \[ B. \[ B . \[ W = \frac{P -

Mar 10, 2025 by ADMIN 216 views

The Formula for the Perimeter of a Rectangle: Solving for Width

The formula for the perimeter of a rectangle is given by ${$ P = 2l + 2w $}$, where ${$ P $}$ represents the perimeter, ${$ l $}$ is the length, and ${$ w $}$ is the width. In this article, we will solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$. This will help us understand the relationship between the perimeter, length, and width of a rectangle.

The formula ${$ P = 2l + 2w $}$ can be broken down into two parts: ${$ 2l $}$ and ${$ 2w $}$. The first part, ${$ 2l $}$, represents twice the length of the rectangle, while the second part, ${$ 2w $}$, represents twice the width of the rectangle. The sum of these two parts gives us the perimeter of the rectangle.

To solve for ${$ w $}$, we need to isolate ${$ w $}$ on one side of the equation. We can start by subtracting ${$ 2l $}$ from both sides of the equation:

${$ P - 2l = 2w $}$

Next, we can divide both sides of the equation by ${$ 2 $}$ to get:

${$ \frac{P - 2l}{2} = w $}$

However, this is not the correct solution. We need to simplify the equation further.

To solve for ${$ w $}$, we can start by subtracting ${$ 2l $}$ from both sides of the equation:

${$ P - 2l = 2w $}$

Next, we can divide both sides of the equation by ${$ 2 $}$ to get:

${$ \frac{P - 2l}{2} = w $}$

However, we can simplify the equation further by multiplying both sides of the equation by ${$ \frac{1}{2} $}$:

${$ w = \frac{P - 2l}{2} $}$

This is the correct solution.

In this article, we solved for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$ using the formula ${$ P = 2l + 2w $}$. We started by subtracting ${$ 2l $}$ from both sides of the equation and then divided both sides of the equation by ${$ 2 $}$. Finally, we simplified the equation further by multiplying both sides of the equation by ${$ \frac{1}{2} $}$. The correct solution is ${$ w = \frac{P - 2l}{2} $}$.

What is the relationship between the perimeter, length, and width of a rectangle?
How can we use the formula ${$ P = 2l + 2w $}$ to solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$?
What is the correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$?

A. ${$ w = P - 2 - l $}$ is incorrect.

B. ${$ w = \frac{P - 2l}{2} $}$ is the correct solution.

For more information on the formula for the perimeter of a rectangle, see Wikipedia.
For more information on solving equations, see Khan Academy.
For more information on algebra, see Mathway.
The Formula for the Perimeter of a Rectangle: Q&A

In our previous article, we solved for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$ using the formula ${$ P = 2l + 2w $}$. In this article, we will answer some frequently asked questions about the formula for the perimeter of a rectangle.

Q: What is the formula for the perimeter of a rectangle? A: The formula for the perimeter of a rectangle is ${$ P = 2l + 2w $}$, where ${$ P $}$ represents the perimeter, ${$ l $}$ is the length, and ${$ w $}$ is the width.

Q: How can I use the formula to solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$? A: To solve for ${$ w $}$, you can start by subtracting ${$ 2l $}$ from both sides of the equation. Then, you can divide both sides of the equation by ${$ 2 $}$ to get ${$ w = \frac{P - 2l}{2} $}$.

Q: What is the relationship between the perimeter, length, and width of a rectangle? A: The perimeter of a rectangle is equal to twice the sum of its length and width. This means that if you know the length and width of a rectangle, you can use the formula to find the perimeter.

Q: Can I use the formula to solve for ${$ l $}$ in terms of ${$ P $}$ and ${$ w $}$? A: Yes, you can use the formula to solve for ${$ l $}$ in terms of ${$ P $}$ and ${$ w $}$. To do this, you can start by subtracting ${$ 2w $}$ from both sides of the equation. Then, you can divide both sides of the equation by ${$ 2 $}$ to get ${$ l = \frac{P - 2w}{2} $}$.

Q: What is the correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$? A: The correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$ is ${$ w = \frac{P - 2l}{2} $}$.

Q: Can I use the formula to solve for ${$ P $}$ in terms of ${$ l $}$ and ${$ w $}$? A: Yes, you can use the formula to solve for ${$ P $}$ in terms of ${$ l $}$ and ${$ w $}$. To do this, you can start by adding ${$ 2l $}$ and ${$ 2w $}$ to both sides of the equation. Then, you can divide both sides of the equation by ${$ 2 $}$ to get ${$ P = l + w $}$.

In this article, we answered some frequently asked questions about the formula for the perimeter of a rectangle. We covered topics such as how to use the formula to solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$, the relationship between the perimeter, length, and width of a rectangle, and how to use the formula to solve for ${$ l $}$ and ${$ P $}$ in terms of ${$ w $}$ and ${$ l $}$ and ${$ w $}$.

What is the relationship between the perimeter, length, and width of a rectangle?
How can I use the formula to solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$?
What is the correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$?

Q: What is the formula for the perimeter of a rectangle? A: The formula for the perimeter of a rectangle is ${$ P = 2l + 2w $}$.
Q: How can I use the formula to solve for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$? A: To solve for ${$ w $}$, you can start by subtracting ${$ 2l $}$ from both sides of the equation. Then, you can divide both sides of the equation by ${$ 2 $}$ to get ${$ w = \frac{P - 2l}{2} $}$.
Q: What is the relationship between the perimeter, length, and width of a rectangle? A: The perimeter of a rectangle is equal to twice the sum of its length and width.
Q: Can I use the formula to solve for ${$ l $}$ in terms of ${$ P $}$ and ${$ w $}$? A: Yes, you can use the formula to solve for ${$ l $}$ in terms of ${$ P $}$ and ${$ w $}$.
Q: What is the correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$? A: The correct solution for ${$ w $}$ in terms of ${$ P $}$ and ${$ l $}$ is ${$ w = \frac{P - 2l}{2} $}$.
Q: Can I use the formula to solve for ${$ P $}$ in terms of ${$ l $}$ and ${$ w $}$? A: Yes, you can use the formula to solve for ${$ P $}$ in terms of ${$ l $}$ and ${$ w $}$.

For more information on the formula for the perimeter of a rectangle, see Wikipedia.
For more information on solving equations, see Khan Academy.
For more information on algebra, see Mathway.