In ∆ABC, D and E are points on sides AB and AC, respectively, such that DE || BC and AD : DB = 3: 1. If EA = 3.3 cm, then find the value of AC.

In ΔABC , D and E are points on sides AB and AC respectively such that DE∥BC.

The ratio AD : DB = 3 : 1.

EA = 3.3cm.

Since DE∥BC, by the Basic Proportionality Theorem (Thales' Theorem), the ratio of the segments on the sides of the triangle will be the same:

​$$\frac{AD}{DB} = \frac{AE}{EC}$$​​

By Thales theorem:

​$$\frac{AE}{EC}=\frac{AD}{DB}\\ \ \\\frac{3.3}{\text{EC}} = \frac{3}{1} \\ \ \\\implies \text{EC} = 1.1 \, cm$$​​

Now, AC = AE + EC = 3.3 + 1.1 = 4.4 cm

Thus, The length of AC is 4.4 cm.