A) 10 cm.
B) 6 cm.
C) 5 cm.
D) 9 cm.
Correct Answer: B
Solution :
CD || AB \[\angle CDE=\angle EAB\] \[\angle DCE=\angle EBA\] By AA-similarity, \[\Delta CDE\sim \Delta BAE\] \[\therefore \]\[\frac{DE}{AE}=\frac{CE}{BE}\] If \[CE=x\,cm,\]then \[\frac{15}{10}=\frac{x}{15-x}\] \[\Rightarrow \]\[\frac{3}{2}=\frac{x}{15-x}\] \[\Rightarrow \]\[2x=45-3x\] \[\Rightarrow \]\[2x+3x=45\] \[\Rightarrow \]\[5x=45\] \[x=\frac{45}{5}=9\,cm.\]You need to login to perform this action.
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