The problem shown in the image asks for the perimeter of a rectangle. The dimensions of the rectangle are given as:

• One pair of sides is $2x$.
• The other pair of sides is $x + 12$.

To calculate the perimeter of a rectangle, the formula is:

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

In this case, the length is $x + 12$ and the width is $2x$.

Substituting the values into the formula:

$P = 2((x + 12) + 2x)$

Now, simplify the expression:

$P = 2(3x + 12) = 6x + 24$

Thus, the perimeter of the rectangle is $6x + 24$. However, this answer does not match any of the provided options (30x or 8x + 24). There might be a discrepancy between the visual information or scaling in the diagram. Based on the formula and the data, the perimeter should be $6x + 24$.

Would you like to clarify this, or should we recheck something else?

Here are five questions that expand on this topic:

1. How does changing the value of $x$ affect the perimeter of the rectangle?
2. What would be the area of the rectangle given these dimensions?
3. How do you calculate the perimeter of a non-rectangular shape?
4. Can the same formula for perimeter be applied to other polygons?
5. What is the difference between perimeter and area in terms of practical applications?

Tip: Always double-check the given dimensions in a geometry problem, especially if a diagram is not to scale.