Analyze the figure shown below in which DE || BC and the other dimensions are as follows: AD=3 cm, BD=4 cm, AE=4.4 cm and DE=6 cm. Calculate the length (in cm) of BC.

Options

A. 6
B. 8
C. 12
D. 14

Answer

To solve the problem, we will use the properties of similar triangles. Since DE is parallel to BC, triangles ADE and ABC are similar.

### Step-by-Step Solution:

1. **Identify the lengths given in the problem:**
- AD = 3 cm
- BD = 4 cm
- AE = 4.4 cm
- DE = 6 cm

2. **Calculate the length of AB:**
- Since AB = AD + BD,
- AB = 3 cm + 4 cm = 7 cm.

3. **Set up the ratio of the sides of the similar triangles:**
- From the similarity of triangles ADE and ABC, we have:
\[ \frac{AD}{AB} = \frac{DE}{BC} \]

4. **Substitute the known values into the ratio:**
- We know AD = 3 cm, AB = 7 cm, and DE = 6 cm.
- Substitute these values into the ratio:
\[ \frac{3}{7} = \frac{6}{BC} \]

5. **Cross-multiply to solve for BC:**
- Cross-multiplying gives:
\[ 3 \cdot BC = 6 \cdot 7 \]
- This simplifies to:
\[ 3 \cdot BC = 42 \]

6. **Divide both sides by 3 to find BC:**
- Thus,
\[ BC = \frac{42}{3} = 14 \text{ cm} \]

### Final Answer:
The length of BC is **14 cm**.