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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![### Algebraic Expression for Perimeter
#### Problem Statement:
Write the perimeter of the floor plan shown as an algebraic expression in \( x \).
#### Diagram:
The provided diagram illustrates a rectangular floor plan with the following dimensions:
- The length of the top edge is \( x - 8 \).
- The height on the left side of the rectangle is 8.
- The length of the bottom edge is \( x - 5 \).
The diagram is a simple rectangular representation of a floor plan with the mentioned sides labeled accordingly.
#### Perimeter Calculation:
The perimeter of a rectangle is calculated by adding together all the sides. Since the diagram gives us expressions and values for some sides, we can derive the expressions for other sides by recognizing opposite sides of a rectangle are equal.
**Given Data:**
- Top edge = \( x - 8 \)
- Left side = 8
- Bottom edge = \( x - 5 \)
Assuming the right side of the rectangle is equal to the left side (8), and taking the provided expressions for the top and bottom edges, the perimeter \( P \) of the rectangle can be computed as follows:
#### Perimeter Formula:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
#### Length and Width:
- Length (Top edge) = \( x - 8 \)
- Width (Left side) = 8
Therefore:
\[ P = 2 \times ((x - 8) + 8) \]
\[ P = 2 \times (x - 8 + 8) \]
\[ P = 2 \times x \]
\[ P = 2x \]
However, accounting for both top and bottom edges along with both left and right sides:
\[ P = (x - 8) + 8 + (x - 5) + 8 \]
Calculate:
\[ P = x - 8 + 8 + x - 5 + 8 \]
\[ P = x + x - 5 + 8 \]
\[ P = x + x + 3 \]
\[ P = 2x - 5\]
### Summary:
The perimeter of the floor is \( \boxed{2x - 5} \).
#### Help Section:
- **Help me solve this**
- **View an example**
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Transcribed Image Text:### Algebraic Expression for Perimeter
#### Problem Statement:
Write the perimeter of the floor plan shown as an algebraic expression in \( x \).
#### Diagram:
The provided diagram illustrates a rectangular floor plan with the following dimensions:
- The length of the top edge is \( x - 8 \).
- The height on the left side of the rectangle is 8.
- The length of the bottom edge is \( x - 5 \).
The diagram is a simple rectangular representation of a floor plan with the mentioned sides labeled accordingly.
#### Perimeter Calculation:
The perimeter of a rectangle is calculated by adding together all the sides. Since the diagram gives us expressions and values for some sides, we can derive the expressions for other sides by recognizing opposite sides of a rectangle are equal.
**Given Data:**
- Top edge = \( x - 8 \)
- Left side = 8
- Bottom edge = \( x - 5 \)
Assuming the right side of the rectangle is equal to the left side (8), and taking the provided expressions for the top and bottom edges, the perimeter \( P \) of the rectangle can be computed as follows:
#### Perimeter Formula:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
#### Length and Width:
- Length (Top edge) = \( x - 8 \)
- Width (Left side) = 8
Therefore:
\[ P = 2 \times ((x - 8) + 8) \]
\[ P = 2 \times (x - 8 + 8) \]
\[ P = 2 \times x \]
\[ P = 2x \]
However, accounting for both top and bottom edges along with both left and right sides:
\[ P = (x - 8) + 8 + (x - 5) + 8 \]
Calculate:
\[ P = x - 8 + 8 + x - 5 + 8 \]
\[ P = x + x - 5 + 8 \]
\[ P = x + x + 3 \]
\[ P = 2x - 5\]
### Summary:
The perimeter of the floor is \( \boxed{2x - 5} \).
#### Help Section:
- **Help me solve this**
- **View an example**
#### Navigation:
- **Previous**
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