The width of a picture frame is the length. Write an algebraic expression of four terms for the perimeter of the picture frame. Use / as your variable.
The width of a picture frame is the length. Write an algebraic expression of four terms for the perimeter of the picture frame. Use / as your variable.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Algebraic Expression for the Perimeter of a Picture Frame**
*Problem Statement:*
The width of a picture frame is \(\frac{1}{8}\) the length. Write an algebraic expression of four terms for the perimeter of the picture frame. Use \(l\) as your variable.
**Solution:**
1. **Definition of Terms:**
- Let \( l \) represent the length of the picture frame.
- The width \( w \) can be expressed as:
\[
w = \frac{1}{8}l
\]
2. **Perimeter of a Rectangle:**
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2(\text{Length} + \text{Width})
\]
3. **Substitute the Expressions:**
Substitute the expressions for length and width into the perimeter formula:
\[
P = 2(l + \frac{1}{8}l)
\]
4. **Simplify the Expression:**
Combine like terms inside the parentheses:
\[
P = 2(\frac{8}{8}l + \frac{1}{8}l) = 2(\frac{9}{8}l)
\]
Multiply through by 2:
\[
P = \frac{18}{8}l = \frac{9}{4}l
\]
5. **Final Expression:**
Therefore, the algebraic expression for the perimeter of the picture frame is:
\[
P = \frac{9}{4}l
\]
This expression allows you to calculate the perimeter of any picture frame where the width is \(\frac{1}{8}\) the length, using \( l \) as the variable for the length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F227c7398-1da7-4025-a597-49565bff2e8c%2Fe3394a6e-c696-4786-a4c2-065e2ca4ac40%2Ftxhwgye_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Algebraic Expression for the Perimeter of a Picture Frame**
*Problem Statement:*
The width of a picture frame is \(\frac{1}{8}\) the length. Write an algebraic expression of four terms for the perimeter of the picture frame. Use \(l\) as your variable.
**Solution:**
1. **Definition of Terms:**
- Let \( l \) represent the length of the picture frame.
- The width \( w \) can be expressed as:
\[
w = \frac{1}{8}l
\]
2. **Perimeter of a Rectangle:**
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2(\text{Length} + \text{Width})
\]
3. **Substitute the Expressions:**
Substitute the expressions for length and width into the perimeter formula:
\[
P = 2(l + \frac{1}{8}l)
\]
4. **Simplify the Expression:**
Combine like terms inside the parentheses:
\[
P = 2(\frac{8}{8}l + \frac{1}{8}l) = 2(\frac{9}{8}l)
\]
Multiply through by 2:
\[
P = \frac{18}{8}l = \frac{9}{4}l
\]
5. **Final Expression:**
Therefore, the algebraic expression for the perimeter of the picture frame is:
\[
P = \frac{9}{4}l
\]
This expression allows you to calculate the perimeter of any picture frame where the width is \(\frac{1}{8}\) the length, using \( l \) as the variable for the length.
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