https://file.aiquickdraw.com/mathbot/file/1726506102356hs3cehz1.jpg

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.

What is the perimeter of the figure shown below, which is not drawn to scale? Dimensions are given as 2x and x + 12.

Learn how to calculate the perimeter of a rectangle when its sides are given as algebraic expressions (2x and x + 12). This solution involves applying the formula for perimeter and simplifying algebraic terms. Suitable for students in Grades 6-8.

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