\( D \) and \( E \) are points on the sides \( A B \) and \( A C \) respectively of a \( \triang...

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\( D \) and \( E \) are points on the sides \( A B \) and \( A C \) respectively of a \( \triangle A B C \) such that \( D E \| B C \).
Find the value of \( x \), when
(i) \( A D=x \mathrm{~cm}, D B=(x-2) \mathrm{cm} \), \( A E=(x+2) \mathrm{cm} \) and \( E C=(x-1) \mathrm{cm} \).
(ii) \( A D=4 \mathrm{~cm}, D B=(x-4) \mathrm{cm}, A E=8 \mathrm{~cm} \) and \( E C=(3 x-19) \mathrm{cm} \).
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(iii) \( A D=(7 x-4) \mathrm{cm}, A E=(5 x-2) \mathrm{cm}, D B=(3 x+4) \mathrm{cm} \) and \( E C=3 x \mathrm{~cm} \).
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