The perimeter $P$ of a rectangle can be found using the formula:

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

Given:

• The length of the rectangle is $5w + 7$
• The width of the rectangle is $4$

Substitute these values into the formula:

$P = 2 \times ((5w + 7) + 4)$

Simplify the expression inside the parentheses:

$P = 2 \times (5w + 7 + 4)$

$P = 2 \times (5w + 11)$

Now, distribute the 2:

$P = 10w + 22$

Thus, the expression for the perimeter of the rectangle is:

$P = 10w + 22$

Would you like further details on how to solve for specific values, or any other explanation?

Here are some related questions for you:

1. How do you calculate the area of the rectangle using the given dimensions?
2. How would the perimeter change if the width were doubled?
3. How would the length of the rectangle change if $w$ were replaced with $2w$?
4. What happens to the perimeter if the length decreases by 3 units?
5. How do you solve for $w$ if the perimeter is set equal to a constant value?

Tip: When working with perimeter problems, always pay close attention to the units for length and width to avoid errors when combining terms.