A) \[\frac{2}{5}\,\,DE\]
B) \[\frac{5}{2}\,\,DE\]
C) \[\frac{3}{2}\,\,DE\]
D) \[\frac{2}{3}\,\,DE\]
Correct Answer: B
Solution :
As in \[\Delta ADE\] and \[\Delta ABC,\] \[\frac{AD}{AB}=\frac{8}{20}=\frac{2}{5},\frac{AE}{EC}=\frac{6}{15}=\frac{2}{5}\] So, \[\frac{AD}{AB}=\frac{AE}{EC}\] and \[\angle A=\angle A'\] (common) \[\Delta ADE\sim \Delta ABC\] \[\therefore \] \[\frac{DE}{BC}=\frac{AD}{AB}\]\[\Rightarrow \]\[\frac{DE}{BC}=\frac{2}{5}\] \[\Rightarrow \] \[BC=\frac{5}{2}DE\]You need to login to perform this action.
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