Since DE ∥ BC, △ADE ~ △ABC (AA similarity).
$$\frac{AD}{AB} = \frac{DE}{BC}$$
AB = AD + DB = 2 + 3 = 5 cm
$$\frac{DE}{7.5} = \frac{2}{5} \implies DE = \frac{2 \times 7.5}{5} = \mathbf{3 \text{ cm}}$$
Answer: (B) 3
Source: Chapter 6, Section 6.3 (Basic Proportionality Theorem / AA Similarity)
---
Since DE ∥ BC, by AA similarity criterion △ADE ~ △ABC. The key ratio is AD/AB (not AD/BD). Students often mistakenly use AD/BD = 2/3 directly — that gives the wrong answer. Always find the full side AB = AD + DB = 5 cm first, then apply the ratio AD/AB = 2/5 to find DE.