Given two similar triangles, $ABC$ and $DEF$, where $AB=6$, $AC=8$, $DE=9$, and $DF=x$, what is the value of $x$?

• A. $8$
• B. $10$
• C. $14$
• D. $12$

Answer: (D)

Verified step by step guidance

1. Identify the corresponding sides of the similar triangles ABC and DEF. Since the triangles are similar, the sides correspond in order: AB corresponds to DE, and AC corresponds to DF.
2. Write the proportion between the corresponding sides using the similarity ratio: \(\frac{AB}{DE} = \frac{AC}{DF}\).
3. Substitute the known values into the proportion: \(\frac{6}{9} = \frac{8}{x}\).
4. Cross-multiply to solve for \(x\): \$6 \times x = 9 \times 8$.
5. Isolate \(x\) by dividing both sides by 6: \(x = \frac{9 \times 8}{6}\).