A rectangular pool garden measures 21 meters by 34 meters and has a cement walkway around its perimeter, as shown. The width remains constant on all four sides. The garden and walkway have a combined area of 828 square meters.
A rectangular pool garden measures 21 meters by 34 meters and has a cement walkway around its perimeter, as shown. The width remains constant on all four sides. The garden and walkway have a combined area of 828 square meters.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Description: Analyzing a Rectangular Pool Garden Design**
A rectangular pool garden measures 21 meters by 34 meters and features a cement walkway around its perimeter, as illustrated. The width of the walkway remains constant on all sides. Together, the garden and the walkway have a combined area of 828 square meters.
**Diagram Explanation**
- A rectangle labeled inside a larger rectangle represents the pool garden.
- The smaller, inner rectangle shows dimensions of 21 meters (width) by 34 meters (length).
- A border labeled 'w' on all sides represents the uniform width of the walkway.
**Question: Determine the Width of the Walkway**
Which equation can be used to find the walkway's width, \( w \)?
- (21 + 2w)(34 + 2w) = 828
- 21(34)(w)(w) = 828
- 21 + 2w + 34 + 2w = 396
- (21+34)(w+w)=828
Choose the correct equation that represents the total area, including both the garden and the walkway.
**Answer Explanation**
To solve for \( w \), consider the entire area as a larger rectangle, accounting for the additional walkway. The dimensions of the larger rectangle are:
- Length: \( 34 + 2w \)
- Width: \( 21 + 2w \)
The equation representing the total area is:
\[ (21 + 2w)(34 + 2w) = 828 \]
This equation correctly models the situation, taking into account the added width \( w \) of the walkway around all sides.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3f0c16-4bc2-4005-8b34-f5a8ba23d8d8%2F6b86161f-7fb8-4e7f-aa5c-f193d8305f91%2Fd7rpwof_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Description: Analyzing a Rectangular Pool Garden Design**
A rectangular pool garden measures 21 meters by 34 meters and features a cement walkway around its perimeter, as illustrated. The width of the walkway remains constant on all sides. Together, the garden and the walkway have a combined area of 828 square meters.
**Diagram Explanation**
- A rectangle labeled inside a larger rectangle represents the pool garden.
- The smaller, inner rectangle shows dimensions of 21 meters (width) by 34 meters (length).
- A border labeled 'w' on all sides represents the uniform width of the walkway.
**Question: Determine the Width of the Walkway**
Which equation can be used to find the walkway's width, \( w \)?
- (21 + 2w)(34 + 2w) = 828
- 21(34)(w)(w) = 828
- 21 + 2w + 34 + 2w = 396
- (21+34)(w+w)=828
Choose the correct equation that represents the total area, including both the garden and the walkway.
**Answer Explanation**
To solve for \( w \), consider the entire area as a larger rectangle, accounting for the additional walkway. The dimensions of the larger rectangle are:
- Length: \( 34 + 2w \)
- Width: \( 21 + 2w \)
The equation representing the total area is:
\[ (21 + 2w)(34 + 2w) = 828 \]
This equation correctly models the situation, taking into account the added width \( w \) of the walkway around all sides.
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