In ΔABC, AB = 20 cm, BC = 7 cm, and AC = 15 cm. Side BC is produced to D such that ΔDAB ~ ΔDCA. The length of the CD is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 9 cm.
DA/DC = AB/CA = DB/DA
Let CD = x cm
BD = BC + CD = (7 + x) cm
DA/DC = AB/CA
⇒ DA/x = 20/15 = 4/3
⇒ DA = (4/3)x
Also, DB/DA = AB/CA
⇒ (7 + x)/[(4/3)x] = 4/3
⇒ 21 + 3x = (16/3)x
⇒ 7x = 63
⇒ x = 9 cm