The algebraic equation for the perimeter $P$ of a rectangle is given by the formula:

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

Since the length is 7 cm and the width is unknown (denoted by $w$), the equation becomes:

$P = 2 \times (7 + w)$

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you solve for $w$ if the perimeter is given?
2. What would the perimeter be if $w = 3$ cm?
3. How does the formula change for the area of the rectangle?
4. What is the perimeter if the width is twice the length?
5. How do we generalize this formula for different shapes?

Tip: Always remember that the perimeter is the total distance around the shape, so you add up all sides!