By Basic Proportionality Theorem (DE || BC):
$$\frac{AD}{DB} = \frac{AE}{EC}$$
DB = AB − AD = 7 − 3 = 4 cm
$$\frac{3}{4} = \frac{AE}{3}$$
$$AE = \frac{9}{4} = 2.25 \text{ cm}$$
Answer: (B) 2.25 cm
Source: Chapter 6, Section 6.3 (Theorem 6.1 — Basic Proportionality Theorem)
Since DE || BC, Thales' theorem gives AD/DB = AE/EC. Students must first find DB = AB − AD = 4 cm, then substitute EC = 3 cm and solve for AE. The common error is using AB instead of DB in the ratio — always use the two segments on the same side (AD and DB), not the full side.