question_answer

Segment AB is parallel to segment CD. AD intersects BC in E. If lengths of AE, BC and ED are 10 cm, 15 cm and 15 cm. what is the length of EC?

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 \[\frac{15}{10}=\frac{x}{15-x}\] \[\Rightarrow \]\[\frac{3}{2}=\frac{x}{15-x}\] \[\Rightarrow \]\[2x=45-3x\] \[\Rightarrow \]\[2x+3x=45\] \[\Rightarrow \]\[5x=45\] \[x=\frac{45}{5}=9\,cm.\]