Solving for the Length of a Rectangle with Given Perimeter and Width
When dealing with problems involving rectangles, it's often necessary to find the dimensions given some known measurements. This tutorial will guide you through solving for the length of a rectangle when the perimeter and width are provided. Let's work through an example to illustrate the process.
Consider the following problem: A rectangular parking lot has a perimeter of 44 yards and a width of 7 yards. What is the length?
Understanding the Formula
The formula for the perimeter of a rectangle is given by:
Perimeter (P) 2 * Length (L) 2 * Width (W)
This can be simplified to:
P 2L 2W
Step-by-Step Solution
Given that the perimeter (P) is 44 yards and the width (W) is 7 yards, we can start by substituting these values into the formula:
44 2L 2 * 7
This simplifies to:
44 2L 14
To isolate the variable (L), we need to subtract 14 from both sides:
44 - 14 2L
30 2L
Finally, we can solve for L by dividing both sides by 2:
L 30 / 2
Therefore, the length (L) is:
L 15 yards
Alternative Solution Methods
There are several ways to arrive at this solution, each offering a different perspective on the mathematical problem. Here are a few alternative solutions:
Solution 1
Using the same formula:
44 2L 2 * 7
This simplifies to:
44 2L 14
Subtracting 14 from both sides:
30 2L
Dividing both sides by 2:
L 30 / 2
L 15 yards
Solution 2
Using the formula:
44 2L 2 * 7
This simplifies to:
44 2L 14
Subtracting 14 from both sides:
30 2L
Dividing both sides by 2:
L 30 / 2
L 15 yards
Solution 3
Using the formula:
44 2L 2 * 7
This simplifies to:
44 2L 14
Subtracting 14 from both sides:
30 2L
Dividing both sides by 2:
L 30 / 2
L 15 yards
Conclusion
By following the steps outlined here, you can easily find the length of a rectangle when given its perimeter and width. The key is to use the perimeter formula correctly and solve for the unknown variable. With practice, these types of problems will become second nature, and you'll be able to tackle more complex geometry problems easily.
Frequently Asked Questions
Q: How do I verify my solution?
A: To verify your solution, plug the value of the length back into the formula and check if the perimeter equals the given value. For example, if the length is 15 yards, the width is 7 yards, and the perimeter is 44 yards, you can verify the solution by checking:
44 2 * 15 2 * 7
44 30 14
44 44
This confirms that your solution is correct.
Q: What is the importance of correctly identifying the variables in the formula?
A: Correctly identifying the variables in the formula is crucial for solving problems accurately. If you misidentify the length or width, your calculations will be incorrect, leading to an incorrect solution. Always double-check which variable represents the length and which represents the width.