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In the​ diagram, there are two similar triangles. Find the unknown measurement.

The diagram shows two similar triangles. The larger triangle has a base of 50 units and a height of 30 units. The smaller triangle, which is inside the larger one, has a base of 22 units, and we need to find its height.

Since the triangles are similar, the corresponding sides of the triangles are proportional. Let's denote the height of the smaller triangle as \( h \).

The proportion between the corresponding sides can be set up as follows:

\[
\frac{\text{Height of smaller triangle}}{\text{Height of larger triangle}} = \frac{\text{Base of smaller triangle}}{\text{Base of larger triangle}}
\]

Substituting the known values:

\[
\frac{h}{30} = \frac{22}{50}
\]

To find \( h \), multiply both sides by 30:

\[
h = \frac{22 \times 30}{50} = \frac{660}{50} = 13.2
\]

So, the height of the smaller triangle is **13.2 units**.

Would you like more details or have any questions about this solution?

Here are five related questions you might find interesting:
1. How do you find the area of similar triangles?
2. What is the relationship between the areas of similar triangles?
3. How would the proportions change if one of the triangles were rotated?
4. Can you apply the concept of similarity to other shapes, like rectangles or circles?
5. How do you determine the scale factor between two similar figures?

**Tip:** When working with similar triangles, always remember that corresponding sides are proportional. This is a powerful tool in solving problems involving similar figures.

Discover how to find the unknown measurement in similar triangles with a step-by-step solution. This problem involves understanding proportionality between corresponding sides of triangles. Suitable for students in Grades 7-9.

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