The perimeter of a rectangle is calculated using the formula:

$P = 2(\text{length} + \text{width})$

Given:

• The length is $x$.
• The width is $x - 6$ (6 units less than the length).

Substitute these into the formula for the perimeter:

$P = 2(x + (x - 6))$

Simplify the expression inside the parentheses:

$P = 2(2x - 6)$

Distribute the 2:

$P = 4x - 12$

Thus, the perimeter of the rectangle is represented by the expression:

$4x - 12$

Would you like me to explain further or clarify any steps?

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Related Questions:

1. What is the perimeter if the length of the rectangle is 10 units?
2. How does the perimeter change if the width is halved instead of reduced by 6 units?
3. How would the expression for the perimeter change if the width were instead twice the length?
4. Can you derive the formula for the area of this rectangle?
5. How does this problem illustrate the relationship between linear expressions and geometry?

Tip:

Always double-check relationships (like "less than" or "greater than") in word problems to ensure you're setting up equations correctly.