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

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

In this case, the width is $t - 8$ centimeters, and the length is $5t + 6$ centimeters.

Substituting these values into the formula for perimeter:

$P = 2(5t + 6) + 2(t - 8)$

Now, distribute the $2$ to both terms inside each set of parentheses:

$P = 2 \times (5t + 6) + 2 \times (t - 8)$ $P = 10t + 12 + 2t - 16$

Now, combine like terms:

$P = (10t + 2t) + (12 - 16)$ $P = 12t - 4$

Thus, the expression that represents the perimeter of the rectangle is:

$P = 12t - 4 \, \text{cm}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the area of a rectangle with the same dimensions?
2. What happens if the width or length of the rectangle becomes negative?
3. Can this expression for perimeter be applied to other shapes? Why or why not?
4. What would the perimeter be if $t = 3$?
5. How does the perimeter change as $t$ increases or decreases?

Tip: Always combine like terms to simplify expressions and make solving easier.