The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then what is the area of the rectangle in square metres?

Introduction / Context:
This question involves a rectangle where you know the difference between length and breadth and the total perimeter. From these two relationships you must find the actual dimensions and then compute the area. It tests your ability to translate verbal information into equations and use basic mensuration formulas, which is very important for aptitude and competitive exams.

Given Data / Assumptions:

- The figure is a rectangle with length l and breadth b measured in metres.
- Length minus breadth is 23 m.
- Perimeter of the rectangle is 206 m.
- We are required to find the area in square metres.
- All sides meet at right angles as in a standard rectangle.

Concept / Approach:
For a rectangle, perimeter P and area A are given by:
- P = 2 * (l + b).
- A = l * b.
The difference l - b = 23 provides one equation, and the perimeter gives the second. Solving these two linear equations provides l and b. Once the dimensions are known, area is found by direct multiplication.

Step-by-Step Solution:
Step 1: Let length = l m and breadth = b m.Step 2: Given l - b = 23.Step 3: Perimeter P = 2 * (l + b) = 206, so l + b = 206 / 2 = 103.Step 4: We now have two equations: l - b = 23 and l + b = 103.Step 5: Add the two equations to eliminate b: (l - b) + (l + b) = 23 + 103 which gives 2l = 126.Step 6: So l = 126 / 2 = 63 m. Substitute into l + b = 103 to get 63 + b = 103, hence b = 40 m.Step 7: Area A = l * b = 63 * 40 = 2520 sq. m.

Verification / Alternative check:
Check the perimeter with the found dimensions: 2 * (63 + 40) = 2 * 103 = 206 m, which matches the given perimeter. Check the difference: 63 - 40 = 23 m, which matches the given difference. Thus, the values are correct and the area 2520 sq. m is consistent.

Why Other Options Are Wrong:
1520 sq. m, 2420 sq. m, 2480 sq. m and 2620 sq. m do not arise from any pair of integer dimensions that simultaneously satisfy both the perimeter and the length minus breadth conditions. They are merely close distractors meant to trap approximate or incorrect calculations.

Common Pitfalls:
One common mistake is to divide the perimeter by 4 to get a single side, which only works for a square. Another is to mis-handle the pair of equations and compute l + b or l - b incorrectly. Forgetting to verify both conditions can also lead to accepting an incorrect pair of dimensions. Always check both the difference and the perimeter before finalising the area.

Final Answer:
Therefore, the area of the rectangle is 2520 sq. m.