Given: BP = 5AP, AC = 54 Formula: If, ΔABC∼ΔPQR, then AB/PQ = BC/QR = AC/PR Calculation: BP = 5AP ⇒ AB = AP + BP ⇒ AB = AP + 5AP ⇒ AB = 6AP In ΔABC and ΔPQA As, PQ||BC hence ΔABC∼ΔPQA Now, AP/AB = AQ/AC ⇒ AP/6AP = AQ/48 ⇒ 1/6 = AQ/54 ⇒ AQ = 54/6 ⇒ AQ = 9 cm