question_answer

In the given figure if \[DE\parallel BC,AE=8\,cm,\,\,EC=2cm\] and \[BC=6\,cm\], then find DE.

Answer:

In \[\Delta \,ADE\] and \[\Delta \,ABC\]

\[\angle DAE=\angle BAC\]                        [Common]

\[\angle ADE=\angle ABC\]                                    [Corresponding angles]

By AA axiom

\[\Delta \,ADE\sim \Delta \,ABC\]

\[\therefore \frac{AE}{AC}=\frac{DE}{BC}\]                   [CPCT]

\[\Rightarrow \frac{8}{8+2}=\frac{DE}{6}\]

\[\Rightarrow 10\,\,DE=48\]

\[\Rightarrow DE=4.8\,\,cm\]