The total area of the four walls of a cuboid room is 400 sq cm. Its length is 15 cm and its height is 8 cm. What is the breadth of the cuboid in centimetres?

Introduction / Context:
This question uses the lateral surface area of a cuboid, sometimes described as the area of the four walls of a room. Given this lateral area and two of the dimensions, you must find the third dimension, which is the breadth. It tests your ability to apply and rearrange the lateral surface area formula for a rectangular prism.

Given Data / Assumptions:

• Lateral surface area (area of 4 walls) = 400 sq cm.
• Length l = 15 cm.
• Height h = 8 cm.
• Breadth b is unknown.
• Formula for area of 4 walls of a cuboid: 2h(l + b).

Concept / Approach:
The area of the four walls of a cuboid excludes the top and bottom faces and equals the perimeter of the base multiplied by the height. The perimeter of the base is 2(l + b), and when multiplied by h, it gives 2h(l + b). We are given that this equals 400 sq cm. By substituting the known values of l and h into this formula, we can solve a simple linear equation for b, the breadth.

Step-by-Step Solution:
Use lateral surface area formula: 2h(l + b) = 400. Substitute h = 8 cm and l = 15 cm. 2 * 8 * (15 + b) = 400. 16 * (15 + b) = 400. Divide both sides by 16: 15 + b = 400 / 16 = 25. So b = 25 - 15 = 10 cm.

Verification / Alternative check:
Verify by recomputing the lateral surface area with length 15 cm, breadth 10 cm and height 8 cm. Perimeter of base = 2 * (15 + 10) = 2 * 25 = 50 cm. Lateral surface area = perimeter of base * height = 50 * 8 = 400 sq cm, which matches the given area, confirming that b = 10 cm is correct.

Why Other Options Are Wrong:
12, 20, 24 and 8: Substituting any of these values for b into 2 * 8 * (15 + b) does not give 400 sq cm. They produce larger or smaller lateral surface areas.

Common Pitfalls:
Using the total surface area formula instead of the lateral surface area formula. Forgetting to multiply by 2 when forming 2h(l + b). Arithmetic mistakes when dividing 400 by 16 or subtracting to find b.

Final Answer:
The breadth of the cuboid is 10 cm