Area of four walls (lateral surface) of a rectangular room is 77 square meters. The room’s length = 7.5 meters and breadth = 3.5 meters. Find the height of the room (assume area of four walls = 2 * height * (length + breadth), ceiling/floor excluded).

Introduction / Context:
For a rectangular room, the “area of four walls” refers to its lateral surface area (LSA). This excludes floor and ceiling and equals the sum of the four vertical faces. Knowing LSA, length, and breadth allows us to solve directly for the room’s height using the standard formula.

Given Data / Assumptions:

• Lateral surface area (four walls) = 77 m^2
• Length l = 7.5 m
• Breadth b = 3.5 m
• Height = h (to be found)
• Formula: LSA = 2 * h * (l + b)

Concept / Approach:
The perimeter of a rectangle made by the walls is 2 * (l + b). Multiplying this by height gives the total vertical area. Rearranging the LSA formula isolates h in one step.

Step-by-Step Solution:
Compute (l + b) = 7.5 + 3.5 = 11LSA = 2 * h * (l + b) ⇒ 77 = 2 * h * 11 = 22hh = 77 / 22 = 3.5 m

Verification / Alternative check:
Back-substitute: 2 * 3.5 * 11 = 77 m^2, matching the given LSA, so the result is consistent.

Why Other Options Are Wrong:
5.4 m, 6.77 m, and 7.7 m would produce lateral areas different from 77 m^2 when used in 22h, so they are inconsistent with the data.

Common Pitfalls:
Confusing LSA with total surface area (which includes floor/ceiling). Here only wall area is intended, so use 2 * h * (l + b).

Final Answer:
3.5 meters