https://r2.erweima.ai/mathbot/image/1725297425059t7oogd35.jpg

En la figura PM=2, AM=3,BC=12 calcular PQ

To solve this problem, we need to calculate the length of \(PQ\) using the given measurements and the relationships in the triangle.

### Given:
- \(PM = 2\)
- \(AM = 3\)
- \(BC = 12\)

### Analyzing the Geometry:
The diagram shows two right triangles that share a common angle at \(A\), suggesting they are similar triangles.

- Triangle \(APM\) is similar to triangle \(ABC\) because they share angle \(A\) and both have a right angle (angle \(PMB\) in triangle \(APM\) and angle \(BCA\) in triangle \(ABC\)).

### Using Similarity of Triangles:
From the similarity of the triangles, we have:
\[
\frac{PM}{AM} = \frac{PQ}{BC}
\]

Substitute the known values:
\[
\frac{2}{3} = \frac{PQ}{12}
\]

### Solving for \(PQ\):
Cross-multiplying gives:
\[
2 \times 12 = 3 \times PQ
\]

\[
24 = 3PQ
\]

\[
PQ = \frac{24}{3} = 8
\]

### Conclusion:
The length of \(PQ\) is 8.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you determine the similarity of triangles?
2. What are some real-life applications of similar triangles?
3. How would the solution change if the triangles were not right triangles?
4. What other geometric properties can be used to solve problems involving triangles?
5. How can trigonometry be applied to solve this problem?

**Tip:** Remember that similarity between triangles helps to set up proportional relationships between their sides, which is a powerful tool for solving many geometric problems.

Learn how to calculate the length of PQ in triangle ABC using the similarity of triangles and proportional relationships. Given PM = 2, AM = 3, BC = 12, find the length of PQ. This problem involves key geometric concepts and is suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation