In a ΔABC, DE is parallel to BC where D and E are the points on AB and AC, respectively and AD = 4 cm, DB = 8 cm, AE = 3 cm. Length of EC is :

5 cm 6 cm 7 cm 9 cm

6 cm

We know that, If ΔABC ∼ ΔADE, then AB/AD = BC/DE = AC/AE We have, AD = 4 cm DB = 8 cm and AE = 3 cm. Now, \(\frac{ AD }{AB}\) = \(\frac{ AE }{AC}\)  = \(\frac{ 4 }{12}\) = \(\frac{ 3 }{AC}\)  = AC = 9cm then, EC = 6 cm