Triangle ABC is such that `AB=9 cm, BC = 6cm, AC = 7.5 cm`. Triangle DEF is similar to `DeltaABC`. If EF = 12 cm then DE is :

Options

A. 6 cm
B. 16 cm
C. 18 cm
D. 15 cm

Answer

To solve the problem, we will use the property of similar triangles, which states that the ratios of corresponding sides of similar triangles are equal.

### Step-by-Step Solution:

1. **Identify the sides of triangle ABC**:
- AB = 9 cm
- BC = 6 cm
- AC = 7.5 cm

2. **Identify the corresponding side in triangle DEF**:
- EF = 12 cm (given)

3. **Set up the proportion using the similarity of triangles**:
Since triangle DEF is similar to triangle ABC, we can write the following proportion:
\[ \frac{DE}{AB} = \frac{EF}{BC} \]

4. **Substitute the known values into the proportion**:
- We know AB = 9 cm and BC = 6 cm, and EF = 12 cm. Therefore, we can substitute these values into the proportion:
\[ \frac{DE}{9} = \frac{12}{6} \]

5. **Simplify the right side of the equation**:
- The fraction \(\frac{12}{6}\) simplifies to 2. Thus, we have:
\[ \frac{DE}{9} = 2 \]

6. **Solve for DE**:
- To find DE, multiply both sides of the equation by 9:
\[ DE = 2 \times 9 = 18 \text{ cm} \]

### Final Answer:
- DE = 18 cm