The Length Of A Rectangle Is Twice Its Width. The Perimeter Is 60 Ft. Find Its Area.A. A = 200 Ft 2 A = 200 \text{ Ft}^2 A = 200 Ft 2 B. A = 100 Ft 2 A = 100 \text{ Ft}^2 A = 100 Ft 2 C. A = 10 Ft 2 A = 10 \text{ Ft}^2 A = 10 Ft 2
Introduction
In this article, we will delve into the world of mathematics, specifically geometry, to solve a problem involving the length and width of a rectangle. The problem states that the length of a rectangle is twice its width, and the perimeter is 60 ft. Our goal is to find the area of this rectangle.
Understanding the Problem
To begin, let's break down the problem and understand what is being asked. We are given a rectangle with an unknown length and width. The length is stated to be twice the width, which we can represent as:
L = 2W
where L is the length and W is the width.
We are also given that the perimeter of the rectangle is 60 ft. The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since a rectangle has two pairs of equal sides, we can represent the perimeter as:
P = 2L + 2W
where P is the perimeter.
Substituting the Given Information
Now that we have the equations for the length and perimeter, we can substitute the given information into these equations. We know that the length is twice the width, so we can substitute L = 2W into the perimeter equation:
P = 2(2W) + 2W P = 4W + 2W P = 6W
We are given that the perimeter is 60 ft, so we can set up the equation:
6W = 60
Solving for the Width
To find the width, we can divide both sides of the equation by 6:
W = 60/6 W = 10
Finding the Length
Now that we have the width, we can find the length by substituting W = 10 into the equation L = 2W:
L = 2(10) L = 20
Calculating the Area
The area of a rectangle is calculated by multiplying the length and width:
A = L × W A = 20 × 10 A = 200
Conclusion
In this article, we explored a problem involving the length and width of a rectangle. We used the given information to find the width and length, and then calculated the area of the rectangle. The final answer is:
The area of the rectangle is 200 ft^2.
Discussion
This problem is a great example of how mathematical concepts can be applied to real-world scenarios. The concept of perimeter and area is crucial in architecture, engineering, and design. By understanding these concepts, we can create structures that are functional, efficient, and aesthetically pleasing.
Related Topics
- Perimeter and area of rectangles
- Mathematical problem-solving
- Geometry and spatial reasoning
Additional Resources
- Khan Academy: Perimeter and Area of Rectangles
- Mathway: Rectangle Perimeter and Area Calculator
- Wolfram Alpha: Rectangle Perimeter and Area Calculator
The Length of a Rectangle: A Mathematical Exploration - Q&A ===========================================================
Introduction
In our previous article, we explored a problem involving the length and width of a rectangle. We used the given information to find the width and length, and then calculated the area of the rectangle. In this article, we will answer some frequently asked questions related to this problem.
Q&A
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 is the perimeter, L is the length, and W is the width.
Q: How do I find the length of a rectangle if I know the perimeter and the width?
A: To find the length of a rectangle, you can use the formula L = (P - 2W) / 2, where P is the perimeter and W is the width.
Q: What is the relationship between the length and width of a rectangle?
A: The length of a rectangle is twice its width, which can be represented as L = 2W.
Q: How do I calculate the area of a rectangle?
A: To calculate the area of a rectangle, you can use the formula A = L × W, where A is the area, L is the length, and W is the width.
Q: What is the area of the rectangle in the given problem?
A: The area of the rectangle in the given problem is 200 ft^2.
Q: How do I find the width of a rectangle if I know the perimeter and the length?
A: To find the width of a rectangle, you can use the formula W = (P - 2L) / 2, where P is the perimeter and L is the length.
Q: What is the perimeter of the rectangle in the given problem?
A: The perimeter of the rectangle in the given problem is 60 ft.
Q: How do I use the given information to find the width of a rectangle?
A: To find the width of a rectangle, you can use the formula W = 60/6, where 60 is the perimeter and 6 is the coefficient of W in the perimeter equation.
Q: What is the length of the rectangle in the given problem?
A: The length of the rectangle in the given problem is 20 ft.
Conclusion
In this article, we answered some frequently asked questions related to the problem of finding the area of a rectangle. We hope that this Q&A article has provided you with a better understanding of the concepts involved in this problem.
Discussion
This problem is a great example of how mathematical concepts can be applied to real-world scenarios. The concept of perimeter and area is crucial in architecture, engineering, and design. By understanding these concepts, we can create structures that are functional, efficient, and aesthetically pleasing.
Related Topics
- Perimeter and area of rectangles
- Mathematical problem-solving
- Geometry and spatial reasoning
Additional Resources
- Khan Academy: Perimeter and Area of Rectangles
- Mathway: Rectangle Perimeter and Area Calculator
- Wolfram Alpha: Rectangle Perimeter and Area Calculator
Practice Problems
- Find the area of a rectangle with a length of 15 ft and a width of 8 ft.
- Find the perimeter of a rectangle with a length of 20 ft and a width of 10 ft.
- Find the width of a rectangle with a perimeter of 60 ft and a length of 20 ft.
- Find the area of a rectangle with a perimeter of 60 ft and a width of 10 ft.
Answers
- A = 15 × 8 = 120 ft^2
- P = 2(20) + 2(10) = 60 ft
- W = (60 - 2(20)) / 2 = 10 ft
- A = 20 × 10 = 200 ft^2