A Rectangle Has A Width Of $x$ Centimeters And A Perimeter Of $8x$ Centimeters. A Square Has Sides Of Length $\frac{1}{4}$ That Of The Length Of The Rectangle.a) Find The Length Of The Rectangle.b) Find The Perimeter Of The

Introduction

In mathematics, understanding the properties of shapes is crucial for solving various problems. In this article, we will explore the relationship between a rectangle and a square, focusing on their perimeters and lengths. We will use algebraic equations to find the length of the rectangle and the perimeter of the square.

The Rectangle

A rectangle has a width of $x$ centimeters and a perimeter of $8x$ centimeters. To find the length of the rectangle, we need to use the formula for the perimeter of a rectangle, which is $2l + 2w$, where $l$ is the length and $w$ is the width.

Perimeter of a Rectangle

The perimeter of a rectangle is given by the formula:

$$P = 2l + 2w$$

In this case, the perimeter is $8x$, and the width is $x$. We can substitute these values into the formula:

$$8x = 2l + 2x$$

To solve for $l$, we can subtract $2x$ from both sides of the equation:

$$6x = 2l$$

Now, we can divide both sides of the equation by $2$ to find the length of the rectangle:

$$l = 3x$$

So, the length of the rectangle is $3x$ centimeters.

The Square

A square has sides of length $\frac{1}{4}$ that of the length of the rectangle. Since the length of the rectangle is $3x$ centimeters, the length of each side of the square is:

$$\frac{1}{4} \times 3x = \frac{3x}{4}$$

Perimeter of the Square

The perimeter of a square is given by the formula:

$$P = 4s$$

where $s$ is the length of each side. In this case, the length of each side is $\frac{3x}{4}$, so we can substitute this value into the formula:

$$P = 4 \times \frac{3x}{4}$$

Simplifying the equation, we get:

$$P = 3x$$

So, the perimeter of the square is $3x$ centimeters.

Conclusion

In this article, we explored the relationship between a rectangle and a square, focusing on their perimeters and lengths. We used algebraic equations to find the length of the rectangle and the perimeter of the square. The length of the rectangle is $3x$ centimeters, and the perimeter of the square is $3x$ centimeters.

Frequently Asked Questions

• What is the perimeter of a rectangle?
• How do you find the length of a rectangle?
• What is the perimeter of a square?
• How do you find the perimeter of a square?

Answer Key

• The perimeter of a rectangle is given by the formula: $P = 2l + 2w$
• To find the length of a rectangle, you need to use the formula: $l = \frac{P - 2w}{2}$
• The perimeter of a square is given by the formula: $P = 4s$
• To find the perimeter of a square, you need to multiply the length of each side by 4.

Additional Resources

• For more information on the perimeter of a rectangle, visit Math Open Reference.
• For more information on the perimeter of a square, visit Math Is Fun.

Final Thoughts

Understanding the properties of shapes is crucial for solving various problems in mathematics. In this article, we explored the relationship between a rectangle and a square, focusing on their perimeters and lengths. By using algebraic equations, we were able to find the length of the rectangle and the perimeter of the square. We hope that this article has provided you with a better understanding of the properties of shapes and how to use algebraic equations to solve problems.

Introduction

In our previous article, we explored the relationship between a rectangle and a square, focusing on their perimeters and lengths. We used algebraic equations to find the length of the rectangle and the perimeter of the square. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the perimeter of a rectangle?

A: The perimeter of a rectangle is given by the formula: $P = 2l + 2w$, where $l$ is the length and $w$ is the width.

Q: How do you find the length of a rectangle?

A: To find the length of a rectangle, you need to use the formula: $l = \frac{P - 2w}{2}$, where $P$ is the perimeter and $w$ is the width.

Q: What is the perimeter of a square?

A: The perimeter of a square is given by the formula: $P = 4s$, where $s$ is the length of each side.

Q: How do you find the perimeter of a square?

A: To find the perimeter of a square, you need to multiply the length of each side by 4: $P = 4s$.

Q: What is the relationship between the length of a rectangle and the length of a square?

A: The length of a square is $\frac{1}{4}$ that of the length of a rectangle.

Q: How do you find the length of a square if you know the length of a rectangle?

A: To find the length of a square, you need to multiply the length of the rectangle by $\frac{1}{4}$: $s = \frac{1}{4} \times l$.

Q: What is the perimeter of a rectangle with a width of $x$ centimeters and a perimeter of $8x$ centimeters?

A: The perimeter of the rectangle is $8x$ centimeters, so the length of the rectangle is $3x$ centimeters. The perimeter of the rectangle is given by the formula: $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Substituting the values, we get: $8x = 2(3x) + 2x$, which simplifies to $8x = 8x$. Therefore, the perimeter of the rectangle is indeed $8x$ centimeters.

Q: What is the perimeter of a square with sides of length $\frac{3x}{4}$ centimeters?

A: The perimeter of the square is given by the formula: $P = 4s$, where $s$ is the length of each side. Substituting the value, we get: $P = 4 \times \frac{3x}{4}$, which simplifies to $P = 3x$ centimeters.

Conclusion

In this article, we answered some frequently asked questions related to the topic of a rectangle and a square. We hope that this article has provided you with a better understanding of the properties of shapes and how to use algebraic equations to solve problems.

Frequently Asked Questions

• What is the perimeter of a rectangle?
• How do you find the length of a rectangle?
• What is the perimeter of a square?
• How do you find the perimeter of a square?
• What is the relationship between the length of a rectangle and the length of a square?
• How do you find the length of a square if you know the length of a rectangle?
• What is the perimeter of a rectangle with a width of $x$ centimeters and a perimeter of $8x$ centimeters?
• What is the perimeter of a square with sides of length $\frac{3x}{4}$ centimeters?

Answer Key

• The perimeter of a rectangle is given by the formula: $P = 2l + 2w$
• To find the length of a rectangle, you need to use the formula: $l = \frac{P - 2w}{2}$
• The perimeter of a square is given by the formula: $P = 4s$
• To find the perimeter of a square, you need to multiply the length of each side by 4
• The length of a square is $\frac{1}{4}$ that of the length of a rectangle
• To find the length of a square, you need to multiply the length of the rectangle by $\frac{1}{4}$
• The perimeter of a rectangle with a width of $x$ centimeters and a perimeter of $8x$ centimeters is $8x$ centimeters
• The perimeter of a square with sides of length $\frac{3x}{4}$ centimeters is $3x$ centimeters

Additional Resources

• For more information on the perimeter of a rectangle, visit Math Open Reference.
• For more information on the perimeter of a square, visit Math Is Fun.

Final Thoughts

Understanding the properties of shapes is crucial for solving various problems in mathematics. In this article, we answered some frequently asked questions related to the topic of a rectangle and a square. We hope that this article has provided you with a better understanding of the properties of shapes and how to use algebraic equations to solve problems.