In figure-2, `DE||BC`. If `(AD)/(DB)=(3)/(2)` and `AE=2.7` cm then `EC` is equal to

Options

A. 2.0 cm
B. 1.8 cm
C. 4.0 cm
D. 2.7 cm

Answer

To solve the problem, we will use the Basic Proportionality Theorem (also known as Thales' theorem), which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

### Step-by-step Solution:

1. **Identify Given Information:**
- We are given that \( DE \parallel BC \).
- The ratio \( \frac{AD}{DB} = \frac{3}{2} \).
- The length \( AE = 2.7 \) cm.
- We need to find \( EC \).

2. **Apply the Basic Proportionality Theorem:**
- According to the theorem, since \( DE \parallel BC \), we can write:
\[ \frac{AD}{DB} = \frac{AE}{EC} \]
- Substituting the known values:
\[ \frac{3}{2} = \frac{2.7}{EC} \]

3. **Cross-Multiply to Solve for \( EC \):**
- Cross-multiplying gives:
\[ 3 \cdot EC = 2 \cdot 2.7 \]
- Simplifying the right side:
\[ 3 \cdot EC = 5.4 \]

4. **Isolate \( EC \):**
- Divide both sides by 3:
\[ EC = \frac{5.4}{3} \]
- Calculating the division:
\[ EC = 1.8 \text{ cm} \]

5. **Conclusion:**
- Therefore, the length of \( EC \) is \( 1.8 \) cm.

### Final Answer:
\( EC = 1.8 \) cm.