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

In the provided diagram, we have two similar triangles. The similarity of the triangles means that the corresponding sides of the triangles are proportional. The lengths of some sides are provided, and we are asked to find the unknown side.

Let's denote the following:
- The base of the smaller triangle is \( x = 10 \).
- The height of the smaller triangle is \( y = 24 \).
- The base of the larger triangle is \( 15 \) (this side corresponds to the base of the smaller triangle).
- The height of the larger triangle (which corresponds to the height of the smaller triangle) is the unknown measurement \( h \).

Given that the triangles are similar, the ratio of corresponding sides should be equal:
\[
\frac{\text{base of smaller triangle}}{\text{base of larger triangle}} = \frac{\text{height of smaller triangle}}{\text{height of larger triangle}}
\]
Substituting the given values:
\[
\frac{10}{15} = \frac{24}{h}
\]

We solve this proportion for \( h \) by cross-multiplying:
\[
10h = 15 \times 24
\]
\[
10h = 360
\]
\[
h = \frac{360}{10} = 36
\]

Thus, the unknown measurement, which is the height of the larger triangle, is \( 36 \).

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

Here are some related questions you might find helpful:
1. How can you determine if two triangles are similar?
2. What are the properties of similar triangles?
3. How do you use proportional relationships to solve problems in geometry?
4. Can you find the area of the triangles in this problem?
5. How does triangle similarity apply in real-world situations?

**Tip:** When working with similar triangles, always ensure that you correctly match corresponding sides and angles to set up accurate proportions.

Explore how to find the unknown measurement in similar triangles with a step-by-step solution. Understand the concept of triangle similarity and proportional relationships. Suitable for Grades 7-9 students studying geometry.

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