What Is The Perimeter, \[$ P \$\], Of A Rectangle That Has A Length Of \[$ X+8 \$\] And A Width Of \[$ Y-1 \$\]?A. \[$ P = 2x + 2y + 18 \$\]B. \[$ P = 2x + 2y + 14 \$\]C. \[$ P = X + Y - 9 \$\]D. \[$
Understanding the Basics of Perimeter
The perimeter of a rectangle is a fundamental concept in mathematics that is used to calculate the total distance around the shape. In this article, we will explore the perimeter of a rectangle with a length of { x+8 $}$ and a width of { y-1 $}$. We will also examine the different options provided to determine the correct formula for the perimeter.
What is the Perimeter Formula?
The perimeter formula for a rectangle is given by { P = 2l + 2w $}$, where { l $}$ is the length and { w $}$ is the width. In this case, the length is { x+8 $}$ and the width is { y-1 $}$.
Calculating the Perimeter
To calculate the perimeter, we need to substitute the values of the length and width into the formula. This gives us:
{ P = 2(x+8) + 2(y-1) $}$
Expanding the Equation
To simplify the equation, we need to expand the terms. This gives us:
{ P = 2x + 16 + 2y - 2 $}$
Combining Like Terms
We can combine the like terms to simplify the equation further. This gives us:
{ P = 2x + 2y + 14 $}$
Evaluating the Options
Now that we have calculated the perimeter, we can evaluate the options provided. The correct formula for the perimeter is:
{ P = 2x + 2y + 14 $}$
This matches option B.
Conclusion
In conclusion, the perimeter of a rectangle with a length of { x+8 $}$ and a width of { y-1 $}$ is given by the formula { P = 2x + 2y + 14 $}$. This formula is derived from the basic perimeter formula for a rectangle and is used to calculate the total distance around the shape.
Frequently Asked Questions
- What is the perimeter of a rectangle?
- How do you calculate the perimeter of a rectangle?
- What is the formula for the perimeter of a rectangle?
Answers
- The perimeter of a rectangle is the total distance around the shape.
- To calculate the perimeter, you need to substitute the values of the length and width into the formula.
- The formula for the perimeter of a rectangle is { P = 2l + 2w $}$, where { l $}$ is the length and { w $}$ is the width.
Additional Resources
- For more information on the perimeter of a rectangle, please visit the following websites:
- Math is Fun
- Khan Academy
References
About the Author
Frequently Asked Questions
Q: What is the perimeter of a rectangle?
A: The perimeter of a rectangle is the total distance around the shape. It is calculated by adding up the lengths of all four sides.
Q: How do you calculate the perimeter of a rectangle?
A: To calculate the perimeter of a rectangle, you need to substitute the values of the length and width into the formula: { P = 2l + 2w $}$, where { l $}$ is the length and { w $}$ is the width.
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 { l $}$ is the length and { w $}$ is the width.
Q: How do you find the perimeter of a rectangle with a length of { x+8 $}$ and a width of { y-1 $}$?
A: To find the perimeter of a rectangle with a length of { x+8 $}$ and a width of { y-1 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x+8) + 2(y-1) $}$. This simplifies to { P = 2x + 2y + 14 $}$.
Q: What is the perimeter of a rectangle with a length of 10 and a width of 5?
A: To find the perimeter of a rectangle with a length of 10 and a width of 5, you need to substitute the values of the length and width into the formula: { P = 2(10) + 2(5) $}$. This simplifies to { P = 20 + 10 $}$, which equals 30.
Q: How do you find the perimeter of a rectangle with a length of 15 and a width of 8?
A: To find the perimeter of a rectangle with a length of 15 and a width of 8, you need to substitute the values of the length and width into the formula: { P = 2(15) + 2(8) $}$. This simplifies to { P = 30 + 16 $}$, which equals 46.
Q: What is the perimeter of a rectangle with a length of { x-3 $}$ and a width of { y+2 $}$?
A: To find the perimeter of a rectangle with a length of { x-3 $}$ and a width of { y+2 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x-3) + 2(y+2) $}$. This simplifies to { P = 2x - 6 + 2y + 4 $}$, which equals { P = 2x + 2y - 2 $}$.
Q: How do you find the perimeter of a rectangle with a length of 20 and a width of 10?
A: To find the perimeter of a rectangle with a length of 20 and a width of 10, you need to substitute the values of the length and width into the formula: { P = 2(20) + 2(10) $}$. This simplifies to { P = 40 + 20 $}$, which equals 60.
Q: What is the perimeter of a rectangle with a length of { x+5 $}$ and a width of { y-4 $}$?
A: To find the perimeter of a rectangle with a length of { x+5 $}$ and a width of { y-4 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x+5) + 2(y-4) $}$. This simplifies to { P = 2x + 10 + 2y - 8 $}$, which equals { P = 2x + 2y + 2 $}$.
Q: How do you find the perimeter of a rectangle with a length of 12 and a width of 6?
A: To find the perimeter of a rectangle with a length of 12 and a width of 6, you need to substitute the values of the length and width into the formula: { P = 2(12) + 2(6) $}$. This simplifies to { P = 24 + 12 $}$, which equals 36.
Q: What is the perimeter of a rectangle with a length of { x-2 $}$ and a width of { y+1 $}$?
A: To find the perimeter of a rectangle with a length of { x-2 $}$ and a width of { y+1 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x-2) + 2(y+1) $}$. This simplifies to { P = 2x - 4 + 2y + 2 $}$, which equals { P = 2x + 2y - 2 $}$.
Q: How do you find the perimeter of a rectangle with a length of 18 and a width of 12?
A: To find the perimeter of a rectangle with a length of 18 and a width of 12, you need to substitute the values of the length and width into the formula: { P = 2(18) + 2(12) $}$. This simplifies to { P = 36 + 24 $}$, which equals 60.
Q: What is the perimeter of a rectangle with a length of { x+1 $}$ and a width of { y-3 $}$?
A: To find the perimeter of a rectangle with a length of { x+1 $}$ and a width of { y-3 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x+1) + 2(y-3) $}$. This simplifies to { P = 2x + 2 + 2y - 6 $}$, which equals { P = 2x + 2y - 4 $}$.
Q: How do you find the perimeter of a rectangle with a length of 15 and a width of 9?
A: To find the perimeter of a rectangle with a length of 15 and a width of 9, you need to substitute the values of the length and width into the formula: { P = 2(15) + 2(9) $}$. This simplifies to { P = 30 + 18 $}$, which equals 48.
Q: What is the perimeter of a rectangle with a length of { x-1 $}$ and a width of { y+4 $}$?
A: To find the perimeter of a rectangle with a length of { x-1 $}$ and a width of { y+4 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x-1) + 2(y+4) $}$. This simplifies to { P = 2x - 2 + 2y + 8 $}$, which equals { P = 2x + 2y + 6 $}$.
Q: How do you find the perimeter of a rectangle with a length of 20 and a width of 15?
A: To find the perimeter of a rectangle with a length of 20 and a width of 15, you need to substitute the values of the length and width into the formula: { P = 2(20) + 2(15) $}$. This simplifies to { P = 40 + 30 $}$, which equals 70.
Q: What is the perimeter of a rectangle with a length of { x+6 $}$ and a width of { y-2 $}$?
A: To find the perimeter of a rectangle with a length of { x+6 $}$ and a width of { y-2 $}$, you need to substitute the values of the length and width into the formula: { P = 2(x+6) + 2(y-2) $}$. This simplifies to { P = 2x + 12 + 2y - 4 $}$, which equals { P = 2x + 2y + 8 $}$.
Q: How do you find the perimeter of a rectangle with a length of 12 and a width of 18?
A: To find the perimeter of a rectangle with a length of 12 and a width of 18, you need to substitute the values of the length and width into the formula: { P = 2(12) + 2(18) $}$. This simplifies to { P = 24 + 36 $}$, which equals 60.
Q: What is the perimeter of a rectangle with a length of { x-4 $}$ and a width of { y+3 $}$?
A: To find the perimeter of a rectangle with a length of