In the figure, DE ∥ BC in △ABC. Given AD = 1.7 cm, AB = 6.8 cm, AC = 9 cm. Find AE (in cm).

Introduction / Context:When a segment DE is drawn parallel to BC in △ABC, triangles ADE and ABC are similar (Basic Proportionality Theorem/Thales). Corresponding sides are proportional.

Given Data / Assumptions:

• DE ∥ BC ⇒ △ADE ∼ △ABC.
• AD = 1.7, AB = 6.8, AC = 9.
• Need AE.

Concept / Approach:Use the similarity ratio AD/AB = AE/AC to compute AE directly.

Step-by-Step Solution:

Verification / Alternative check:Scale factor from big to small is 0.25 (since AD is one-fourth of AB); then AE must be one-fourth of AC, i.e., 2.25 cm.

Why Other Options Are Wrong:They correspond to using wrong sides or inverting the ratio; only 2.25 cm respects the similarity scale factor consistently.

Common Pitfalls:Using BD/BC or mixing sides from different triangles; misreading AD/AB as AB/AD.

Final Answer:2.25cm