The total area of the four walls of a rectangular room (excluding floor and ceiling) is 57 m². The room has length 5.5 m and height 3 m. Using the formula for the lateral surface area of a cuboid, what is the breadth (in m) of the room?

Introduction:
This question tests the application of surface area formulas for a cuboid, specifically the lateral (four walls) surface area. Given the area of the four walls, length, and height, we can determine the missing breadth of the room.

Given Data / Assumptions:

• Room is a rectangular cuboid.
• Length l = 5.5 m.
• Height h = 3 m.
• Area of four walls (lateral surface area) = 57 m².
• We must find breadth b (in metres).

Concept / Approach:
For a cuboid with length l, breadth b, and height h, the total area of the four vertical walls (lateral surface area) is: Lateral area = 2h(l + b). This is because there are two walls of dimension l by h and two walls of dimension b by h. With lateral area known, we can solve for b.

Step-by-Step Solution:
Given lateral area = 57 m². Use formula: 2h(l + b) = 57. Substitute h = 3, l = 5.5: 2 * 3 * (5.5 + b) = 57. This simplifies to 6(5.5 + b) = 57. Divide both sides by 6: 5.5 + b = 57 / 6 = 9.5. So b = 9.5 − 5.5 = 4 m.

Verification / Alternative check:
Check the result by recomputing the lateral area: l + b = 5.5 + 4 = 9.5. Then 2h(l + b) = 2 * 3 * 9.5 = 6 * 9.5 = 57 m², which matches the given lateral surface area exactly.

Why Other Options Are Wrong:
If breadth were 3 m, 3.5 m, or 4.5 m, the lateral area would be different from 57 m². For example, with b = 3, we get 2 * 3 * (5.5 + 3) = 49.5 m², not 57 m². Only b = 4 m yields the correct lateral area.

Common Pitfalls:
Students often confuse total surface area (including floor and ceiling) with lateral area. Others mistakenly use formula 2(lb + bh + lh). Here the question clearly specifies four walls only, so we must use 2h(l + b). Clarifying what surfaces are included avoids such confusion.

Final Answer:
The breadth of the room is 4 m.