A hospital ward must accommodate 56 patients so that each gets 2.2 m^2 of floor area and 8.8 m^3 of air space. If the room length is fixed at 14 m, find the required breadth and height.

Introduction / Context:The ward must satisfy two constraints simultaneously: adequate floor area and adequate air volume. With a fixed length, we determine breadth from floor-area needs and then height from the volume requirement.

Given Data / Assumptions:

• Patients = 56.
• Per-patient floor area = 2.2 m^2.
• Per-patient volume = 8.8 m^3.
• Length L = 14 m.

Concept / Approach:

• Total floor area A = 56 * 2.2.
• Total volume V = 56 * 8.8.
• Let breadth = B and height = H. Then A = L*B and V = L*B*H.

Step-by-Step Solution:

Verification / Alternative check:Check both constraints: floor area = 14*8.8 = 123.2 m^2 ✓; volume = 14*8.8*4 = 492.8 m^3 ✓. Both satisfied exactly.

Why Other Options Are Wrong:

• 8.4 m, 4.2 m and others: Either floor area or volume misses the requirements.
• None of these: Not applicable since (8.8 m, 4 m) meets both constraints exactly.

Common Pitfalls:

• Confusing per-patient values with totals.
• Solving only the area constraint and forgetting to verify volume.

Final Answer:8.8 m, 4 m