Let ΔABC ~ ΔQPR and (Area of ΔABC) : (Area of ΔPQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB ?

19.8 cm

As ΔABC ~ ΔQPR

So, \( {AB }^{2 } \)/\( {QP }^{2 } \) = 121/64

⇒ \(\frac{AB}{QP}\) = \(\frac{11}{8}\)

⇒ \(\frac{AB}{14.4}\) = \(\frac{11}{8}\)

⇒ 8AB = 11 x 14.4

⇒ AB = \(\frac{11\;  × \;14.4}{8}\)

⇒ AB = 19.8 cm

Therefore, the length of AB is 19.8 cm.