https://file.aiquickdraw.com/mathbot/file/1726967371507y08hiwbh.jpg

The image shows two triangles, and it appears that they are similar based on the angles marked in each triangle.

### Step 1: Identifying the sides of similar triangles
The larger triangle has sides labeled as 12 and 8, while the smaller triangle has sides labeled as \( 2x \) and \( x + 2 \).

Since these triangles are similar, the corresponding sides are proportional. The ratio of the corresponding sides of the larger triangle to the smaller triangle can be set up as follows:

\[
\frac{12}{2x} = \frac{8}{x + 2}
\]

### Step 2: Solving the proportion
Now, cross-multiply to solve for \( x \):

\[
12(x + 2) = 8(2x)
\]

Expanding both sides:

\[
12x + 24 = 16x
\]

### Step 3: Isolating \( x \)
Move all terms involving \( x \) to one side:

\[
24 = 16x - 12x
\]

Simplify:

\[
24 = 4x
\]

Solve for \( x \):

\[
x = \frac{24}{4} = 6
\]

Thus, the value of \( x \) is 6.

Let me know if you'd like further details or have any questions. Here are some related questions for practice:

1. What is the definition of similar triangles?
2. How do you verify that two triangles are similar?
3. Can you solve for a different side ratio in the same problem?
4. How would the solution change if one triangle was not similar to the other?
5. What are the properties of proportional sides in similar triangles?

**Tip:** When dealing with similar triangles, always set up corresponding side ratios to solve for unknown variables efficiently.

Solve for x in the given triangles where the larger triangle has sides 12 and 8, and the smaller triangle has sides 2x and x + 2. The triangles are similar.

Solve for x using similar triangles with proportional sides. Learn how to apply the AA similarity theorem and set up side ratios in triangles with sides 12, 8, 2x, and x + 2. Includes step-by-step solution for Grades 7-10.

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