**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.

The width of a picture frame is 18 the length. To write an algebraic expression of four terms for…

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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.

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