Equal-area relation gives altitude on a different side: In triangle ABC, side BC = 10 cm and the altitude from A to BC (AD) is 4.4 cm. If AC = 11 cm, find the altitude from B to AC (i.e., BE).

Introduction / Context:
The area of a triangle can be expressed using any side as base and its corresponding altitude. Equating these expressions lets us transfer from one altitude to another.

Given Data / Assumptions:

• |BC| = 10 cm
• Altitude AD to BC = 4.4 cm
• |AC| = 11 cm

Concept / Approach:
Area via base BC: A = (1/2) * BC * AD. Also A = (1/2) * AC * BE. Equate and solve BE = (BC * AD) / AC.

Step-by-Step Solution:
A = (1/2) * 10 * 4.4 = 22 sq cm22 = (1/2) * 11 * BE ⇒ BE = (44) / 11 = 4 cm

Verification / Alternative check:
Units consistent (cm for lengths, sq cm for area). Both formulas return the same area.

Why Other Options Are Wrong:
5 cm, 5.5 cm, and 5.6 cm do not satisfy the area equality with given sides.

Common Pitfalls:
Forgetting that area remains constant regardless of base/altitude choice, or mixing which altitude corresponds to which base.

Final Answer:
4 cm