The perimeter of a rectangle is 60 centimetres and its breadth is 14 centimetres. Find the area of the rectangle in square centimetres.

Introduction / Context:
This problem involves finding the dimensions and area of a rectangle when its perimeter and one side are known. It checks your ability to use the perimeter formula and then compute area once both length and breadth are determined. Rectangular geometry of this type is very common in aptitude tests.

Given Data / Assumptions:

• Perimeter of rectangle P = 60 centimetres.
• Breadth B = 14 centimetres.
• Length L is unknown.
• We must find the area A = L * B in square centimetres.

Concept / Approach:
The perimeter P of a rectangle with length L and breadth B is given by:
P = 2 * (L + B).
We can rearrange this to express L in terms of P and B: L + B = P / 2, so L = P / 2 - B. Once we find L, we multiply L and B to obtain the area. This is a straightforward application of perimeter and area formulas.

Step-by-Step Solution:
Step 1: Use the perimeter formula P = 2 * (L + B). Given P = 60 and B = 14, we have 60 = 2 * (L + 14). Step 2: Divide both sides by 2: 60 / 2 = L + 14. So 30 = L + 14. Step 3: Solve for L: L = 30 - 14 = 16 centimetres. Step 4: Area A = L * B = 16 * 14. 16 * 14 = 224 square centimetres.

Verification / Alternative check:
We can check by recomputing the perimeter from L and B. With L = 16 cm and B = 14 cm, perimeter P = 2 * (16 + 14) = 2 * 30 = 60 centimetres. This matches the given perimeter, confirming that our length and area are correct. The area of 224 cm2 is therefore consistent with both the given data and the rectangle formulas.

Why Other Options Are Wrong:
Option A (112 cm2): This might come from mistakenly using half the correct length or breadth in the area formula. Option B (448 cm2): This is exactly double the correct area and could result from an incorrect multiplication or unit mistake. Option D (336 cm2): This suggests a wrong length value was used with correct breadth. Option E (196 cm2): This equals 14 * 14, which assumes the rectangle is a square with side 14, which does not satisfy the given perimeter.

Common Pitfalls:
Students sometimes confuse the formula for perimeter with that for area, or they forget to divide the perimeter by 2 when solving for L + B. Another mistake is to miscalculate 16 * 14. Writing each algebraic step clearly and checking the final perimeter helps prevent errors.

Final Answer:
The area of the rectangle is 224 cm2 (square centimetres).