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A rectangular garden measures 24 ft by 37 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path. Be sure to include correct unit in your answer.

A rectangular garden measures 24 ft by 37 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path. Be sure to include correct unit in your answer.

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 Statement:** A rectangular garden measures 24 ft by 37 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path. Be sure to include the correct unit in your answer. **Solution:** 1. First, calculate the area of the garden, which is a rectangle: - Length = 37 ft - Width = 24 ft - Area of the garden (A_garden) = Length x Width = 37 ft x 24 ft = 888 ft² 2. To find the total area including the path, note that the width of the path is 3 ft, extending along all sides of the garden. This means the length and width of the entire garden including the path are: - New Length = 37 ft + 2 x 3 ft = 37 ft + 6 ft = 43 ft - New Width = 24 ft + 2 x 3 ft = 24 ft + 6 ft = 30 ft - Total Area (A_total) = New Length x New Width = 43 ft x 30 ft = 1290 ft² 3. To find the area of the path alone (A_path), subtract the area of the garden from the total area: - A_path = A_total - A_garden = 1290 ft² - 888 ft² = 402 ft² **Answer:** The area of the path is 402 ft².
Transcribed Image Text:**Problem Statement:** A rectangular garden measures 24 ft by 37 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path. Be sure to include the correct unit in your answer. **Solution:** 1. First, calculate the area of the garden, which is a rectangle: - Length = 37 ft - Width = 24 ft - Area of the garden (A_garden) = Length x Width = 37 ft x 24 ft = 888 ft² 2. To find the total area including the path, note that the width of the path is 3 ft, extending along all sides of the garden. This means the length and width of the entire garden including the path are: - New Length = 37 ft + 2 x 3 ft = 37 ft + 6 ft = 43 ft - New Width = 24 ft + 2 x 3 ft = 24 ft + 6 ft = 30 ft - Total Area (A_total) = New Length x New Width = 43 ft x 30 ft = 1290 ft² 3. To find the area of the path alone (A_path), subtract the area of the garden from the total area: - A_path = A_total - A_garden = 1290 ft² - 888 ft² = 402 ft² **Answer:** The area of the path is 402 ft².
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