The Perimeter Of A Rectangle Is 16 Inches. The Equation That Represents This Is 2 L + 2 W = 16 2l + 2w = 16 2 L + 2 W = 16 , Where L L L Represents The Length Of The Rectangle And W W W Is The Width.What Value Is Possible For The Length Of The Rectangle?A. 7

Introduction

In geometry, the perimeter of a rectangle is the total distance around its edges. It is a fundamental concept that is used to calculate the dimensions of various shapes and objects. In this article, we will explore the relationship between the length and width of a rectangle, given its perimeter. We will use the equation $2l + 2w = 16$ to determine the possible values for the length of the rectangle.

The Equation: $2l + 2w = 16$

The equation $2l + 2w = 16$ represents the perimeter of a rectangle, where $l$ is the length and $w$ is the width. To understand this equation, let's break it down:

• The perimeter of a rectangle is equal to the sum of the lengths of all its sides.
• Since a rectangle has two pairs of equal sides (length and width), we can represent the perimeter as $2l + 2w$.
• The equation states that the perimeter is equal to 16 inches.

Solving for Length

To find the possible values for the length of the rectangle, we need to isolate the variable $l$ in the equation. We can do this by subtracting $2w$ from both sides of the equation:

$2l + 2w = 16$

Subtracting $2w$ from both sides:

$2l = 16 - 2w$

Dividing both sides by 2:

$l = 8 - w$

This equation shows that the length of the rectangle is equal to 8 minus the width.

Possible Values for Length

Now that we have the equation $l = 8 - w$, we can find the possible values for the length of the rectangle. Since the width $w$ can take any value between 0 and 8 (inclusive), we can substitute different values of $w$ into the equation to find the corresponding values of $l$.

Width ($w$)	Length ($l$)
0	8
1	7
2	6
3	5
4	4
5	3
6	2
7	1
8	0

As we can see, the possible values for the length of the rectangle are 8, 7, 6, 5, 4, 3, 2, 1, and 0 inches.

Conclusion

In conclusion, the equation $2l + 2w = 16$ represents the perimeter of a rectangle, where $l$ is the length and $w$ is the width. By solving for length, we found that the length of the rectangle is equal to 8 minus the width. We then used this equation to find the possible values for the length of the rectangle, which are 8, 7, 6, 5, 4, 3, 2, 1, and 0 inches.

Discussion

What value is possible for the length of the rectangle?

A. 7

The correct answer is A. 7. This is because when the width $w$ is 1, the length $l$ is equal to 7 (as shown in the table above).

Additional Questions

1. What is the perimeter of a rectangle with a length of 4 inches and a width of 3 inches?
2. If the perimeter of a rectangle is 20 inches, what is the length of the rectangle if the width is 4 inches?
3. What is the width of a rectangle with a length of 6 inches and a perimeter of 18 inches?

Answer Key

1. The perimeter of a rectangle with a length of 4 inches and a width of 3 inches is 14 inches.
2. If the perimeter of a rectangle is 20 inches and the width is 4 inches, the length is 6 inches.
3. The width of a rectangle with a length of 6 inches and a perimeter of 18 inches is 3 inches.
   The Perimeter of a Rectangle: Q&A =====================================

Q: What is the perimeter of a rectangle?

A: The perimeter of a rectangle is the total distance around its edges. It is a fundamental concept that is used to calculate the dimensions of various shapes and objects.

Q: How do I calculate the perimeter of a rectangle?

A: To calculate the perimeter of a rectangle, you need to add up the lengths of all its sides. Since a rectangle has two pairs of equal sides (length and width), you can represent the perimeter as $2l + 2w$, where $l$ is the length and $w$ is the width.

Q: What is the equation for the perimeter of a rectangle?

A: The equation for the perimeter of a rectangle is $2l + 2w = 16$, where $l$ is the length and $w$ is the width.

Q: How do I solve for length in the equation $2l + 2w = 16$?

A: To solve for length, you need to isolate the variable $l$ in the equation. You can do this by subtracting $2w$ from both sides of the equation:

$2l + 2w = 16$

Subtracting $2w$ from both sides:

$2l = 16 - 2w$

Dividing both sides by 2:

$l = 8 - w$

Q: What are the possible values for the length of the rectangle?

A: The possible values for the length of the rectangle are 8, 7, 6, 5, 4, 3, 2, 1, and 0 inches.

Q: How do I find the width of a rectangle if I know its length and perimeter?

A: To find the width of a rectangle, you need to use the equation $w = 8 - l$, where $l$ is the length and $w$ is the width.

Q: What is the perimeter of a rectangle with a length of 4 inches and a width of 3 inches?

A: The perimeter of a rectangle with a length of 4 inches and a width of 3 inches is 14 inches.

Q: If the perimeter of a rectangle is 20 inches, what is the length of the rectangle if the width is 4 inches?

A: If the perimeter of a rectangle is 20 inches and the width is 4 inches, the length is 6 inches.

Q: What is the width of a rectangle with a length of 6 inches and a perimeter of 18 inches?

A: The width of a rectangle with a length of 6 inches and a perimeter of 18 inches is 3 inches.

Q: Can I use the equation $2l + 2w = 16$ to find the perimeter of a rectangle with a length of 5 inches and a width of 2 inches?

A: Yes, you can use the equation $2l + 2w = 16$ to find the perimeter of a rectangle with a length of 5 inches and a width of 2 inches. Simply substitute the values of $l$ and $w$ into the equation and solve for the perimeter.

Q: What is the perimeter of a rectangle with a length of 5 inches and a width of 2 inches?

A: The perimeter of a rectangle with a length of 5 inches and a width of 2 inches is 14 inches.

Q: Can I use the equation $w = 8 - l$ to find the width of a rectangle with a length of 3 inches?

A: Yes, you can use the equation $w = 8 - l$ to find the width of a rectangle with a length of 3 inches. Simply substitute the value of $l$ into the equation and solve for the width.

Q: What is the width of a rectangle with a length of 3 inches?

A: The width of a rectangle with a length of 3 inches is 5 inches.

Conclusion

In conclusion, the perimeter of a rectangle is a fundamental concept that is used to calculate the dimensions of various shapes and objects. The equation $2l + 2w = 16$ represents the perimeter of a rectangle, where $l$ is the length and $w$ is the width. By solving for length, we found that the length of the rectangle is equal to 8 minus the width. We then used this equation to find the possible values for the length of the rectangle, which are 8, 7, 6, 5, 4, 3, 2, 1, and 0 inches.