Homework Help is Here – Start Your Trial Now!
Math
Geometry
Español A rectangular garden measures 31 ft by 47 ft. Surrounding (and bordering) the garden is a path 2 ft wide. Find the area of this path. Be sure to include the correct unit in your answer. 0 ft X ft² S ft³

Español A rectangular garden measures 31 ft by 47 ft. Surrounding (and bordering) the garden is a path 2 ft wide. Find the area of this path. Be sure to include the correct unit in your answer. 0 ft X ft² S ft³

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
See similar textbooks
icon
Related questions
Question
**Problem Statement:** A rectangular garden measures 31 feet by 47 feet. Surrounding (and bordering) the garden is a path 2 feet wide. Find the area of this path. Be sure to include the correct unit in your answer. **Answer Box:** [ ] **Unit Selection:** - ft - ft² - ft³ Selection box includes options for choosing the correct unit: ft, ft², ft³. --- To solve this problem, follow these steps: 1. **Calculate the dimensions of the garden including the path:** - Length with path: \( 47 + 4 = 51 \) feet - Width with path: \( 31 + 4 = 35 \) feet (We add 4 feet because the path is 2 feet wide on all sides.) 2. **Find the area of the garden including the path:** \[ Area_{garden + path} = 51 \, \text{ft} \times 35 \, \text{ft} = 1,785 \, \text{ft}^2 \] 3. **Find the area of the garden without the path:** \[ Area_{garden} = 47 \, \text{ft} \times 31 \, \text{ft} = 1,457 \, \text{ft}^2 \] 4. **Calculate the area of the path:** \[ Area_{path} = Area_{garden + path} - Area_{garden} \] \[ Area_{path} = 1,785 \, \text{ft}^2 - 1,457 \, \text{ft}^2 = 328 \, \text{ft}^2 \] **Correct Unit:** ft² Thus, the area of the path is \( 328 \, \text{ft}^2 \). Be sure to input your answer and select the correct unit using the options provided.
Transcribed Image Text:**Problem Statement:** A rectangular garden measures 31 feet by 47 feet. Surrounding (and bordering) the garden is a path 2 feet wide. Find the area of this path. Be sure to include the correct unit in your answer. **Answer Box:** [ ] **Unit Selection:** - ft - ft² - ft³ Selection box includes options for choosing the correct unit: ft, ft², ft³. --- To solve this problem, follow these steps: 1. **Calculate the dimensions of the garden including the path:** - Length with path: \( 47 + 4 = 51 \) feet - Width with path: \( 31 + 4 = 35 \) feet (We add 4 feet because the path is 2 feet wide on all sides.) 2. **Find the area of the garden including the path:** \[ Area_{garden + path} = 51 \, \text{ft} \times 35 \, \text{ft} = 1,785 \, \text{ft}^2 \] 3. **Find the area of the garden without the path:** \[ Area_{garden} = 47 \, \text{ft} \times 31 \, \text{ft} = 1,457 \, \text{ft}^2 \] 4. **Calculate the area of the path:** \[ Area_{path} = Area_{garden + path} - Area_{garden} \] \[ Area_{path} = 1,785 \, \text{ft}^2 - 1,457 \, \text{ft}^2 = 328 \, \text{ft}^2 \] **Correct Unit:** ft² Thus, the area of the path is \( 328 \, \text{ft}^2 \). Be sure to input your answer and select the correct unit using the options provided.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS