Math Problem Statement
A rectangular garden measures 23 ft by 35 ft. Surrounding (and bordering) the garden is a path 3 ft wide. Find the area of this path.
Solution
To solve this problem, we need to calculate the area of the path surrounding the garden. Here's how:
Step 1: Dimensions of the garden
The garden is a rectangle with dimensions:
- Length =
- Width =
Step 2: Dimensions of the garden including the path
The path is wide and surrounds the garden. Adding this width to all sides:
- New length (including the path) =
- New width (including the path) =
Step 3: Total area including the path
The total area of the garden and path is:
Step 4: Area of the garden
The area of the garden (without the path) is:
Step 5: Area of the path
The area of the path is the total area minus the garden area:
Final Answer:
The area of the path is 384 ft².
Would you like further clarification on this solution?
Follow-Up Questions:
- How is the concept of area extended when the path is non-rectangular?
- What happens to the path area if the garden has irregular dimensions?
- How can this problem be solved using algebraic expressions for different path widths?
- How would the solution change if the path only surrounded two sides of the garden?
- What real-life scenarios use similar calculations (e.g., fencing or landscaping)?
Tip:
Always double-check units to ensure consistency in your calculations!
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of Rectangles
Subtraction of Areas
Formulas
Area of a rectangle = length × width
New dimensions = original dimensions + 2 × path width
Path area = Total area - Garden area
Theorems
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Suitable Grade Level
Grades 6-8