Two triangles, \( \triangle ABC \) and \( \triangle DEF \), are similar. The lengths of the sides of \( \triangle ABC \) are 6 cm, 8 cm, and 10 cm, and the lengths of the sides of \( \triangle DEF \) are \( 9 \) cm, \( 12 \) cm, and \( x \) cm. Determine the value of \( x \). Let's think step by step and output the final answer within \boxed{}.
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