Correct option is (B) 2.1 cm
\(\because\) DE || BC in \(\triangle ABC\)
\(\therefore\) \(\triangle ADE\sim\triangle ABC\) (As DE || BC \(\Rightarrow\) Corresponding angles are equal)
\(\therefore\) \(\frac{AD}{AB} = \frac{AE}{AC}\) _______________(1)
Given that \(\frac{AD}{DB} = \frac{3}{5}\)
\(\Rightarrow BD=\frac53AD\)
\(\because AB=AD+BD\)
\(=AD+\frac53AD=\frac83AD\)
\(\therefore\) \(\frac{AD}{AB} = \frac{3}{8}\)
Then from (1), \(\frac{AE}{AC}=\frac38\)
\(\Rightarrow AE=\frac38AC\)
\(=\frac{3}{8}\times5.6\) \((\because AC=5.6\,cm)\)
\(=3\times0.7\)
= 2.1 cm
