The area of the four walls of a cuboid room (lateral surface area) is 57 sq m. If its length is 5.5 m and its height is 3 m, what is the breadth of the cuboid (in metres)?

Introduction / Context:
This question deals with the lateral surface area of a cuboid, which corresponds to the area of its four vertical walls. For practical applications, such as painting or wallpapering a room, this lateral area is more important than the total surface area. Knowing the relationship between the lateral surface area and the dimensions of a cuboid allows us to find unknown dimensions when sufficient information is provided.

Given Data / Assumptions:

• The solid is a cuboid (rectangular box).
• The area of the four walls (lateral surface area) is 57 square metres.
• Length (l) of the cuboid is 5.5 m.
• Height (h) of the cuboid is 3 m.
• We must find the breadth (b) in metres.

Concept / Approach:
The lateral surface area (area of the four walls) of a cuboid of length l, breadth b, and height h is given by:
Lateral area = 2h(l + b) This formula comes from adding the areas of the four rectangles: two of size l * h and two of size b * h. We substitute the known values of lateral area, length, and height and then solve for breadth b.

Step-by-Step Solution:
Step 1: Write the formula for lateral surface area: L = 2h(l + b). Step 2: Substitute L = 57 sq m, h = 3 m, and l = 5.5 m. Step 3: The equation becomes 57 = 2 * 3 * (5.5 + b). Step 4: Simplify the constant product: 2 * 3 = 6, so 57 = 6 * (5.5 + b). Step 5: Divide both sides by 6: (5.5 + b) = 57 / 6. Step 6: Compute 57 / 6 = 9.5. Step 7: So 5.5 + b = 9.5. Step 8: Solve for b: b = 9.5 - 5.5 = 4. Step 9: Hence, the breadth is 4 metres.

Verification / Alternative check:
We can quickly verify by plugging b = 4 back into the formula. Then l + b = 5.5 + 4 = 9.5. Lateral area becomes 2 * 3 * 9.5 = 6 * 9.5 = 57 sq m, which matches the given value. Thus the breadth of 4 m is consistent with all the information provided.

Why Other Options Are Wrong:

• 4.5, 3, 3.5, and 2.5: Substituting any of these into l + b would not produce 9.5, and therefore the lateral surface area would not equal 57 sq m. These are distractors arising from algebraic or arithmetic mistakes.

Common Pitfalls:
One common error is to use the total surface area formula instead of the lateral surface area formula, leading to extra terms such as 2lb that are not needed. Another pitfall is miscalculating the division or the product 2h(l + b). Carefully substituting values and solving the simple linear equation step by step helps avoid such mistakes.

Final Answer:
Therefore, the breadth of the cuboid is 4 m.