The problem involves a rectangular sandbox with a specific relationship between its length and width. We need to express its perimeter using an algebraic expression....
Key Concepts
Before we dive into the solution, let's clarify some essential concepts:
- Rectangle: A quadrilateral with four right angles and opposite sides equal in length.
- Perimeter: The total distance around the outside of a shape.
- Algebraic Expression: A combination of variables, constants, and mathematical operations.
Finding the Perimeter
Here's how to find the perimeter of the sandbox:
- Identify the dimensions:
- Width (w) = w inches
- Length (l) = 1.5w inches (since length is 1.5 times the width)
- Perimeter formula: The perimeter of a rectangle is calculated as: Perimeter = 2 * (length + width)
- Substitute the dimensions: Perimeter = 2 * (1.5w + w)
- Simplify: Perimeter = 2 * (2.5w) = 5w
The Expression
Therefore, the expression representing the perimeter of the sandbox is 5w, where 'w' is the width of the sandbox in inches.
Example
Let's say the width of the sandbox is 10 inches (w = 10). Then, the perimeter would be: 5 * 10 = 50 inches.
Conclusion
By understanding the relationship between the length and width of the sandbox and applying the perimeter formula, we have successfully derived an algebraic expression to represent its perimeter. This expression is concise and allows us to calculate the perimeter easily for any given width.