The Perimeter of a Rectangle

Oct 13, 2025 by leolavanderia.com.br 120 views

Introduction

In this problem, we are given the relationship between the length and width of a rectangle and its perimeter. We need to determine the dimensions of the rectangle using the given information. To solve this problem, we will use algebraic equations to represent the relationships between the length, width, and perimeter of the rectangle.

Given Information

The length of the rectangle is 3 more than twice the width.
The perimeter of the rectangle is 132 cm.

Let's Represent the Length and Width Algebraically

Let's use the following variables to represent the length and width of the rectangle:

L = length of the rectangle
W = width of the rectangle

We are given that the length of the rectangle is 3 more than twice the width. We can write this relationship as an equation:

L = 2W + 3

The Perimeter of a Rectangle

The perimeter of a rectangle is the sum of the lengths of all its sides. The formula for the perimeter of a rectangle is:

Perimeter = 2(L + W)

We are given that the perimeter of the rectangle is 132 cm. We can substitute this value into the formula:

132 = 2(L + W)

Simplifying the Equation

We can simplify the equation by dividing both sides by 2:

66 = L + W

Substituting the Relationship Between L and W

We can substitute the relationship between L and W into the simplified equation:

66 = (2W + 3) + W

Combine Like Terms

We can combine like terms:

66 = 3W + 3

Subtract 3 from Both Sides

We can subtract 3 from both sides:

63 = 3W

Divide Both Sides by 3

We can divide both sides by 3:

21 = W

Find the Value of L

Now that we have found the value of W, we can substitute it into the equation L = 2W + 3:

L = 2(21) + 3

L = 42 + 3

L = 45

Conclusion

In this problem, we used algebraic equations to represent the relationships between the length, width, and perimeter of a rectangle. We found the dimensions of the rectangle by substituting the given information into the equations and solving for the values of L and W. The final answer is:

L = 45 cm
W = 21 cm

The Final Answer

$The final answer is: $\boxed{45, 21}$<br/> **Determine the Equations to Use for the Given Rectangle Problem**$

Q&A: Rectangle Problem

Q: What is the relationship between the length and width of the rectangle? A: The length of the rectangle is 3 more than twice the width.

Q: How can we represent the length and width algebraically? A: We can use the following variables to represent the length and width of the rectangle:

L = length of the rectangle
W = width of the rectangle

Q: What is the formula for the perimeter of a rectangle? A: The formula for the perimeter of a rectangle is:

Perimeter = 2(L + W)

Q: How can we simplify the equation 132 = 2(L + W)? A: We can simplify the equation by dividing both sides by 2:

66 = L + W

Q: How can we substitute the relationship between L and W into the simplified equation? A: We can substitute the relationship between L and W into the simplified equation:

66 = (2W + 3) + W

Q: How can we combine like terms in the equation 66 = (2W + 3) + W? A: We can combine like terms:

66 = 3W + 3

Q: How can we find the value of W in the equation 66 = 3W + 3? A: We can subtract 3 from both sides:

63 = 3W

Then, we can divide both sides by 3:

21 = W

Q: How can we find the value of L in the equation L = 2W + 3? A: We can substitute the value of W into the equation:

L = 2(21) + 3

L = 42 + 3

L = 45

Q: What are the dimensions of the rectangle? A: The dimensions of the rectangle are:

L = 45 cm
W = 21 cm

Q: What is the perimeter of the rectangle? A: The perimeter of the rectangle is 132 cm.

Q: How can we use algebraic equations to solve this problem? A: We can use algebraic equations to represent the relationships between the length, width, and perimeter of the rectangle. We can then substitute the given information into the equations and solve for the values of L and W.

Conclusion

In this Q&A article, we have discussed the rectangle problem and how to use algebraic equations to solve it. We have found the dimensions of the rectangle and the perimeter of the rectangle. We have also discussed how to use algebraic equations to represent the relationships between the length, width, and perimeter of the rectangle.

The Final Answer

The final answer is: $\boxed{45, 21}$