Explanation:

- Two triangles, ?ABC and ?DEF, are given as similar.

- In similar triangles, corresponding sides are in proportion.

- Given: AB = 6 cm, BC = 8 cm, DE = 9 cm.

- To find EF, set up a proportion with the sides:

$$

\frac{AB}{DE} = \frac{BC}{EF}

$$

- Substitute the values:

$$

\frac{6}{9} = \frac{8}{EF}

$$

- Simplify and solve for EF:

$$

\frac{2}{3} = \frac{8}{EF}

$$

$$

2 \times EF = 24

$$

$$

EF = 12 \, \text{cm}

$$

- Option 1: 12 cm (Correct answer)

- Option 2: 9 cm (Incorrect, EF is not 9 cm)

- Option 3: 10 cm (Incorrect, EF is not 10 cm)

- Option 4: 8 cm (Incorrect, EF is not 8 cm)

Answer: Option 1: 12 cm

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