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13. Mr. Dilbert's rectangular swimming pool is surrounded on all sides by a 4-foot wide brick walkway, as shown below. WALKWAY 19 feet 5 feet What is the area of the walkway?

13. Mr. Dilbert's rectangular swimming pool is surrounded on all sides by a 4-foot wide brick walkway, as shown below. WALKWAY 19 feet 5 feet What is the area of the walkway?

Elementary Geometry For College Students, 7e
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
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### Problem 13: **Context:** Mr. Dilbert's rectangular swimming pool is surrounded on all sides by a 4-foot wide brick walkway. **Diagram Explanation:** - The diagram shows a rectangular swimming pool surrounded by a brick walkway. - The pool itself has dimensions of 19 feet by 5 feet. - The brick walkway is uniformly 4 feet wide on all sides of the pool. **Question:** What is the area of the walkway? **Answer choices:** - A. \(96 \text{ ft}^2\) - B. \(192 \text{ ft}^2\) - C. \(247 \text{ ft}^2\) - D. \(302 \text{ ft}^2\) **Solution Explanation:** 1. First, calculate the dimensions of the entire rectangle (pool plus walkway). The walkway adds 4 feet to each side of the pool: - Length: \(19 + 4 + 4 = 27 \text{ feet}\) - Width: \(5 + 4 + 4 = 13 \text{ feet}\) Therefore, the total dimensions of the rectangle are 27 feet by 13 feet. 2. Calculate the area of the entire rectangle: - \(27 \text{ feet} \times 13 \text{ feet} = 351 \text{ ft}^2\) 3. Calculate the area of the pool: - \(19 \text{ feet} \times 5 \text{ feet} = 95 \text{ ft}^2\) 4. Subtract the area of the pool from the area of the entire rectangle to find the area of the walkway: - \(351 \text{ ft}^2 - 95 \text{ ft}^2 = 256 \text{ ft}^2\) 5. Thus, the area of the walkway is \(\boxed{256 \text{ ft}^2}\). ### Answer: The area of the walkway is \(\boxed{256 \text{ ft}^2}\).
Transcribed Image Text:### Problem 13: **Context:** Mr. Dilbert's rectangular swimming pool is surrounded on all sides by a 4-foot wide brick walkway. **Diagram Explanation:** - The diagram shows a rectangular swimming pool surrounded by a brick walkway. - The pool itself has dimensions of 19 feet by 5 feet. - The brick walkway is uniformly 4 feet wide on all sides of the pool. **Question:** What is the area of the walkway? **Answer choices:** - A. \(96 \text{ ft}^2\) - B. \(192 \text{ ft}^2\) - C. \(247 \text{ ft}^2\) - D. \(302 \text{ ft}^2\) **Solution Explanation:** 1. First, calculate the dimensions of the entire rectangle (pool plus walkway). The walkway adds 4 feet to each side of the pool: - Length: \(19 + 4 + 4 = 27 \text{ feet}\) - Width: \(5 + 4 + 4 = 13 \text{ feet}\) Therefore, the total dimensions of the rectangle are 27 feet by 13 feet. 2. Calculate the area of the entire rectangle: - \(27 \text{ feet} \times 13 \text{ feet} = 351 \text{ ft}^2\) 3. Calculate the area of the pool: - \(19 \text{ feet} \times 5 \text{ feet} = 95 \text{ ft}^2\) 4. Subtract the area of the pool from the area of the entire rectangle to find the area of the walkway: - \(351 \text{ ft}^2 - 95 \text{ ft}^2 = 256 \text{ ft}^2\) 5. Thus, the area of the walkway is \(\boxed{256 \text{ ft}^2}\). ### Answer: The area of the walkway is \(\boxed{256 \text{ ft}^2}\).
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