To solve for $x$ using the concept of similar triangles, let's use the corresponding sides of the triangles and set up a proportion.

Since the triangles are similar, the ratios of corresponding side lengths are equal. This means:

$\frac{4.44}{13.32} = \frac{1.15}{x}$

Now we can solve for $x$ by cross-multiplying.

1. Set up the equation:

$4.44 \times x = 1.15 \times 13.32$

2. Calculate $1.15 \times 13.32$:

$1.15 \times 13.32 = 15.318$

3. Divide by 4.44 to solve for $x$:

$x = \frac{15.318}{4.44} \approx 3.45$

Answer:

The value of $x \approx 3.45$.

Would you like further explanation on the steps? Here are some additional related questions:

1. How can you determine if triangles are similar?
2. What are some real-world applications of similar triangles?
3. How can you use ratios to solve for unknown sides in other shapes?
4. What is the difference between similar and congruent shapes?
5. How can trigonometric ratios help solve similar triangle problems?

Tip: When working with similar triangles, always confirm that angles match up and sides are proportionally related.