Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Problem: Finding the Ratio of Perimeter to Area
#### Given a Rectangle
- **Dimensions:**
- Height: 6 feet
- Width: 4 feet
#### Task
Find the ratio of the perimeter to the area of the given rectangle.
#### Diagram
The diagram shows a rectangle with a height of 6 feet and a width of 4 feet.
### Calculation Steps
1. **Perimeter of the Rectangle:**
- Formula: \( P = 2 \times (\text{height} + \text{width}) \)
- Calculation: \( P = 2 \times (6 \text{ ft} + 4 \text{ ft}) = 2 \times 10 \text{ ft} = 20 \text{ ft} \)
2. **Area of the Rectangle:**
- Formula: \( A = \text{height} \times \text{width} \)
- Calculation: \( A = 6 \text{ ft} \times 4 \text{ ft} = 24 \text{ ft}^2 \)
3. **Ratio of Perimeter to Area:**
- Ratio: \( \frac{P}{A} \)
- Calculation: \( \frac{20 \text{ ft}}{24 \text{ ft}^2} = \frac{20}{24} = \frac{5}{6} \)
### Answer Options
1. \( \frac{2}{3} \)
2. \( \frac{3}{2} \)
3. \( \frac{5}{6} \)
**Correct Answer:**
\[ \frac{5}{6} \]
### User Input
- **Your answer:**
- [ ] \( \frac{2}{3} \)
- [ ] \( \frac{3}{2} \)
- [ ] \( \frac{5}{6} \) (Correct Answer)
This question guides students through the process of finding the ratio of the perimeter to the area of a given rectangle. The provided choices facilitate self-assessment and understanding in geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01b580fa-011d-4ada-be68-942e2d4e7c99%2Fe1422ded-462a-4147-8a6b-dd508aaa1217%2F7zugcfe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem: Finding the Ratio of Perimeter to Area
#### Given a Rectangle
- **Dimensions:**
- Height: 6 feet
- Width: 4 feet
#### Task
Find the ratio of the perimeter to the area of the given rectangle.
#### Diagram
The diagram shows a rectangle with a height of 6 feet and a width of 4 feet.
### Calculation Steps
1. **Perimeter of the Rectangle:**
- Formula: \( P = 2 \times (\text{height} + \text{width}) \)
- Calculation: \( P = 2 \times (6 \text{ ft} + 4 \text{ ft}) = 2 \times 10 \text{ ft} = 20 \text{ ft} \)
2. **Area of the Rectangle:**
- Formula: \( A = \text{height} \times \text{width} \)
- Calculation: \( A = 6 \text{ ft} \times 4 \text{ ft} = 24 \text{ ft}^2 \)
3. **Ratio of Perimeter to Area:**
- Ratio: \( \frac{P}{A} \)
- Calculation: \( \frac{20 \text{ ft}}{24 \text{ ft}^2} = \frac{20}{24} = \frac{5}{6} \)
### Answer Options
1. \( \frac{2}{3} \)
2. \( \frac{3}{2} \)
3. \( \frac{5}{6} \)
**Correct Answer:**
\[ \frac{5}{6} \]
### User Input
- **Your answer:**
- [ ] \( \frac{2}{3} \)
- [ ] \( \frac{3}{2} \)
- [ ] \( \frac{5}{6} \) (Correct Answer)
This question guides students through the process of finding the ratio of the perimeter to the area of a given rectangle. The provided choices facilitate self-assessment and understanding in geometry.
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