To find the perimeter of this rectangle, we will sum up all the sides.

From the image:

• One pair of opposite sides is labeled as $5x - 15$ and $2x - 3$,
• The other pair is labeled as $x - 1$ (opposite sides of a rectangle are equal).

Step 1: Express the perimeter

The perimeter $P$ of a rectangle is calculated by adding all sides or using the formula:

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

From the image, the lengths and widths are:

• Two lengths: $5x - 15$ and $2x - 3$
• Two widths: $x - 1$ (repeated on both sides)

Thus, the perimeter is:

$P = 2\left((5x - 15) + (x - 1)\right)$

Step 2: Simplify the expression for the perimeter

First, combine the terms inside the parentheses:

$P = 2\left((5x - 15) + (x - 1)\right)$ $P = 2\left(5x + x - 15 - 1\right)$ $P = 2\left(6x - 16\right)$

Now, distribute the 2:

$P = 12x - 32$

Step 3: Solve for $x$

If there is a specific value for the perimeter provided (such as a numerical value), we could solve for $x$. However, the image does not specify a perimeter value. If you have this value, you can set the equation equal to that number and solve for $x$.

Would you like to provide a specific perimeter or clarify any other details?

Related Questions:

1. How would the equation change if the rectangle was a square?
2. What happens to the perimeter when $x$ is a negative number?
3. Can you solve for $x$ if the area of the rectangle is given?
4. How does the perimeter change as $x$ increases?
5. What is the difference between finding the perimeter and finding the area in this case?

Tip:

When solving for variables in expressions involving perimeter or area, always combine like terms carefully before substituting or simplifying further.