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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.

The two triangles below are similar. Calculate the value of x. Give your answer as an integer or as a fraction in its simplest form.

Learn how to solve for x using the properties of similar triangles. In this problem, the corresponding sides of two triangles are proportional, and we use the ratio of the sides to calculate the unknown value x. Suitable for students in Grades 7-9.

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