Consider the \( \triangle \mathrm{ABC} \) where \( \mathrm{BC}=12 \mathrm{~cm}, \mathrm{DB}=9 \)...

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Consider the \( \triangle \mathrm{ABC} \) where \( \mathrm{BC}=12 \mathrm{~cm}, \mathrm{DB}=9 \) \( \mathrm{cm}, \mathrm{CD}=6 \mathrm{~cm} \) and \( \angle \mathrm{BCD}=\angle \mathrm{BAC} \). The ratio of the perimeter of the triangle \( \mathrm{ADC} \) to that of triangle BDC is \( \mathrm{k}: \) 9. Find the value of \( \mathrm{k} \).
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