In triangle ABC, DE || BC, where D and E lie on sides AB and AC respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, then find the length of AC.

Q.In triangle ABC, DE || BC, where D and E lie on sides AB and AC respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, then find the length of AC.

In triangle ABC, DE || BC \[ \therefore \cfrac{AD}{DB} = \cfrac{AE}{EC} \quad \text{[By Thales' Theorem]} \] \[ \therefore \cfrac{5}{6} = \cfrac{7.5}{EC} \] \[ \Rightarrow EC = \cfrac{7.5 \times 6}{5} = 9 \, \text{cm} \] \[ \therefore \text{AC} = \text{AE} + \text{EC} = 7.5 + 9 = 16.5 \, \text{cm} \]