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

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

In this case:

• The width of the rectangle is $3b + 5$ cm.
• The length of the rectangle is $8b + 6$ cm.

Substituting these into the perimeter formula:

$P = 2 \times \left( (8b + 6) + (3b + 5) \right)$

First, simplify the expression inside the parentheses:

$P = 2 \times \left( 8b + 3b + 6 + 5 \right)$ $P = 2 \times \left( 11b + 11 \right)$

Now distribute the 2:

$P = 2 \times 11b + 2 \times 11$ $P = 22b + 22$

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

$P = 22b + 22 \text{ cm}$

Would you like more details on this problem, or have any other questions?

Here are 5 related questions:

1. How do you find the perimeter of a rectangle when given both sides?
2. How can the perimeter formula be used to find missing dimensions?
3. What is the perimeter of a rectangle if $b = 2$?
4. How does the perimeter change as $b$ increases?
5. Can the perimeter formula apply to other shapes like squares?

Tip: Always simplify expressions inside parentheses before applying operations like multiplication or distribution.