The perimeter of a rectangle is 48 cm and its breadth is 10 cm. What is the area of the rectangle in square centimetres?

Introduction / Context:
This is another perimeter and area problem for a rectangle, similar in spirit to earlier questions but with different numbers. Such problems are very common in aptitude and school exams because they reinforce the connection between linear measures and area. The main idea is to first find the unknown side using the perimeter and then multiply length and breadth to obtain the area.

Given Data / Assumptions:

• The shape is a rectangle.
• Perimeter P = 48 cm.
• Breadth b = 10 cm.
• Length l is unknown.
• We must find the area A in square centimetres.

Concept / Approach:
The perimeter of a rectangle is given by P = 2 * (l + b). With P and b known, we can solve for l by rearranging this equation. Once l is found, the area is computed using A = l * b. The process involves simple algebra and then straightforward multiplication.

Step-by-Step Solution:
Given P = 48 cm and b = 10 cm.Perimeter formula: P = 2 * (l + b).Substitute values: 48 = 2 * (l + 10).Divide both sides by 2: 24 = l + 10.Solve for l: l = 24 − 10 = 14 cm.Area A = l * b = 14 * 10 = 140 sq cm.

Verification / Alternative check:
Check that these dimensions give the correct perimeter. With l = 14 cm and b = 10 cm, we have P = 2 * (14 + 10) = 2 * 24 = 48 cm, exactly as given. This confirms that l = 14 cm is consistent. Multiplying 14 by 10 again gives 140 sq cm, so the area calculation is correct and matches all conditions in the problem.

Why Other Options Are Wrong:
Option 480 is a confusion of area with the product of perimeter and breadth or some other miscalculation. Option 240 would require l = 24 when breadth is 10, but then perimeter would not be 48. Option 440 is far from any reasonable value in this context. Option 160 would result from using l = 16 with b = 10, which would give perimeter 52, not 48. Only 140 sq cm satisfies both the perimeter condition and the area formula.

Common Pitfalls:
Frequently, students mix up which value is length and which is breadth, but since multiplication is commutative, this usually does not affect area, only the interpretation. The more dangerous mistake is misapplying the perimeter formula and writing P = l * b, or forgetting to divide by 2 when solving 48 = 2 * (l + 10). Being systematic in substituting and solving helps avoid these algebraic mistakes.

Final Answer:
The area of the rectangle is 140 sq cm.