Correct option is (D) 12 cm
In triangles \(\triangle ABE\;and\;\triangle ACD,\) we have
\(\angle BAE=\angle CAD\) (Common angles)
and \(\angle ABE=\angle ACD=90^\circ\) (Given)
\(\therefore\) \(\triangle ABE\sim\triangle ACD\) (By AA similarity rule)
\(\therefore\frac{AB}{AC}=\frac{AE}{AD}=\frac{BE}{CD}\) (Corresponding sides are in the same ratio in similar triangles)
\(\frac{BE}{CD}=\frac{AB}{AC}\)
\(\Rightarrow\) \(\frac{4.5}{CD}=\frac38\) \((\because BE=4.5\,cm,AB=3\,cm\;\&\;AC=8\,cm)\)
\(\Rightarrow CD=\frac{4.5\times8}3\)
\(=1.5\times8=12\,cm\)
