To find the area of the rectangle, we need to first determine the values of the length and width using the given information, and then calculate the area.

Step 1: Set up the equation for perimeter

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

$P = 2(\text{Length} + \text{Width})$

We are told that the perimeter is 130, the length is $3x - 15$, and the width is $x - 8$. Substituting these values into the formula:

$130 = 2\left((3x - 15) + (x - 8)\right)$

Step 2: Solve for $x$

Simplify the equation:

$130 = 2\left(4x - 23\right)$

Divide both sides by 2:

$65 = 4x - 23$

Add 23 to both sides:

$88 = 4x$

Now, divide by 4:

$x = 22$

Step 3: Find the length and width

Now that we have $x = 22$, we can substitute this value back into the expressions for the length and width:

$\text{Length} = 3x - 15 = 3(22) - 15 = 66 - 15 = 51$

$\text{Width} = x - 8 = 22 - 8 = 14$

Step 4: Calculate the area

The area $A$ of a rectangle is given by the formula:

$A = \text{Length} \times \text{Width}$

Substitute the values for the length and width:

$A = 51 \times 14 = 714$

So, the area of the rectangle is $714 \, \text{square units}$.

Would you like further details or clarification? Here are some related questions:

1. What if the perimeter was different? How would it change the area?
2. How does changing $x$ affect the length and width of the rectangle?
3. What is the effect on the perimeter when length or width is doubled?
4. Can we express the area as a function of $x$ before solving for $x$?
5. How would the problem change if we knew the area but not the perimeter?

Tip: Always check if you need to solve for variables first when working with formulas.