The two triangles in the image are similar, meaning their corresponding sides are proportional. To find the value of $x$, we set up a proportion using corresponding sides.

Corresponding sides:

• Small triangle: $15 \, \text{mm}$ and $3 \, \text{mm}$.
• Large triangle: $x \, \text{mm}$ and $10 \, \text{mm}$.

Proportion:

$\frac{15}{3} = \frac{x}{10}.$

Solve for $x$:

1. Simplify the left-hand side: $\frac{15}{3} = 5.$

2. Write the equation: $5 = \frac{x}{10}.$

3. Multiply both sides by $10$ to isolate $x$: $x = 5 \cdot 10.$

4. Calculate: $x = 50.$

Final Answer:

$x = 50 \, \text{mm}.$

Would you like a detailed explanation or have any questions?

Here are 5 related questions:

1. How do we identify corresponding sides in similar triangles?
2. What are other methods to prove that two triangles are similar?
3. If the side ratio changes, how would it affect the calculations for $x$?
4. Can similar triangles have different orientations? How does it affect their comparison?
5. How is the concept of similarity applied in real-world situations?

Tip: Always check the orientation of triangles when determining corresponding sides.