The two triangles $S$ and $T$ are similar, meaning their corresponding sides are proportional. The problem requires us to find the value of $x$ using the sides given.

For triangle $S$:

• Base = 18 mm
• Height = 3 mm

For triangle $T$:

• Base = $x$ mm
• Height = 10 mm

Since the triangles are similar, we can set up the proportion:

$\frac{\text{Base of } S}{\text{Base of } T} = \frac{\text{Height of } S}{\text{Height of } T}$

$\frac{18}{x} = \frac{3}{10}$

Now we cross multiply to solve for $x$:

$18 \times 10 = 3 \times x$

$180 = 3x$

$x = \frac{180}{3}$

$x = 60 \text{ mm}$

So, the value of $x$ is 60 mm.

Would you like a more detailed explanation, or do you have any other questions?

Here are 5 related questions:

1. How do we verify that two triangles are similar?
2. What are the properties of similar triangles?
3. Can we use a different method to find $x$ in this problem?
4. How does the ratio of corresponding sides relate to the areas of similar triangles?
5. What is the relationship between angles in similar triangles?

Tip: When working with similar figures, always remember that corresponding angles are equal, and the lengths of corresponding sides are in proportion.