https://file.aiquickdraw.com/mathbot/file/17262840375263m2qtw7u.jpg

The problem is asking for the length of segment \( AB \) based on the given conditions:

1. \( D \) is the midpoint of segment \( AC \).
2. \( C \) is the midpoint of segment \( DB \).
3. \( AC = 3 \, \text{cm} \).

### Step-by-Step Solution:

1. **Interpretation of Midpoints**:
   - Since \( D \) is the midpoint of \( AC \), it means:
     \[
     AD = DC = \frac{AC}{2} = \frac{3}{2} = 1.5 \, \text{cm}.
     \]
   - Now, \( C \) is the midpoint of \( DB \). So, we need to calculate \( AB \).

2. **Breaking \( AB \) into segments**:
   - \( AB \) can be written as:
     \[
     AB = AD + DB.
     \]
   - From the first condition, we know that \( AD = 1.5 \, \text{cm} \).

3. **Relation between \( DB \) and \( DC \)**:
   - Since \( C \) is the midpoint of \( DB \), it follows that:
     \[
     DC = CB.
     \]
   - We already know that \( DC = 1.5 \, \text{cm} \), which means:
     \[
     DB = DC + CB = 1.5 + 1.5 = 3 \, \text{cm}.
     \]

4. **Final Calculation of \( AB \)**:
   \[
   AB = AD + DB = 1.5 + 3 = 4.5 \, \text{cm}.
   \]

### Conclusion:
The length of segment \( AB \) is \( \boxed{4.5} \, \text{cm} \).

---

Would you like further clarification on any step? Here are some related questions to explore:

1. How do you find the length of a segment when given midpoints?
2. What are the properties of midpoints in geometry?
3. How would the problem change if \( AC \) had a different length?
4. Can you generalize this solution for any length of \( AC \)?
5. How do you apply the midpoint theorem in different geometric contexts?

**Tip:** Always remember that the midpoint divides a line segment into two equal parts. This concept is fundamental when solving geometry problems involving midpoints.

If D is the midpoint of segment AC, C is the midpoint of segment DB, and AC = 3 cm, what is the length of segment AB?

Solve the geometry problem where D is the midpoint of segment AC, C is the midpoint of segment DB, and AC = 3 cm. Learn how to calculate the length of segment AB using midpoint properties and key geometric formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation