Express the perimeter P of a rectangle as a function of the length L if the length of the rectangle is twice its width 

To express the perimeter \( P \) of a rectangle as a function of its length \( L \), given that the length \( L \) is twice its width \( W \), follow these steps:

1. **Relate the width to the length**:  
   Since the length is twice the width, we can write:
   \[
   L = 2W
   \]
   Solving for \( W \) in terms of \( L \):
   \[
   W = \frac{L}{2}
   \]

2. **Express the perimeter**:  
   The perimeter \( P \) of a rectangle is given by the formula:
   \[
   P = 2L + 2W
   \]
   Substitute \( W = \frac{L}{2} \) into the perimeter formula:
   \[
   P = 2L + 2\left(\frac{L}{2}\right)
   \]
   Simplify the expression:
   \[
   P = 2L + L = 3L
   \]

So, the perimeter \( P \) as a function of the length \( L \) is:
\[
P(L) = 3L
\]

Would you like any details or have any questions?

Here are 5 related questions you might find interesting:

1. What is the area of the rectangle as a function of the length \( L \)?
2. If the perimeter is known, how can you find the length \( L \) of the rectangle?
3. How does the relationship between length and width affect the area?
4. How would the formula change if the length were three times the width?
5. What is the diagonal of the rectangle as a function of the length \( L \)?

**Tip:** Always check if dimensions are related when deriving formulas; it simplifies expressions significantly.

Learn how to express the perimeter of a rectangle as a function of its length L. Detailed step-by-step solution with mathematical formulas and explanations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation