The perimeter of a rectangle is 84 m.\nIts length is 6 m more than its breadth.\nWhat is the area of the rectangle in sq m?

Introduction:
This question tests the standard perimeter and area formulas of a rectangle along with a simple linear relation between length and breadth. From the perimeter, we can determine the sum of length and breadth. Since the length is given as a fixed amount more than the breadth, we can solve the two-variable problem using substitution. Once length and breadth are found, the area is simply the product L * B. This is a classic aptitude question that checks whether you correctly interpret “length is 6 m more than breadth” and apply the perimeter formula without mistakes.

Given Data / Assumptions:

• Perimeter P = 84 m
• Length L = B + 6
• Perimeter of rectangle: P = 2(L + B)
• Area of rectangle: A = L * B

Concept / Approach:
Convert perimeter into L + B by dividing by 2. Then use substitution L = B + 6 to find B. Finally compute L and multiply L and B to get the area. This is a direct two-step algebra problem with no unit conversion needed.

Step-by-Step Solution:
2(L + B) = 84 => L + B = 42Given L = B + 6So (B + 6) + B = 422B + 6 = 42 => 2B = 36 => B = 18L = B + 6 = 18 + 6 = 24Area = L * B = 24 * 18 = 432

Verification / Alternative Check:
Check perimeter: 2(24 + 18) = 2*42 = 84 m, correct. Since both constraints match, the dimensions are correct, so area must be 24*18 = 432 sq m. This also aligns with the idea that a rectangle with moderate side lengths should not produce an extremely large or small area relative to its perimeter.

Why Other Options Are Wrong:
330, 333, 360, 362: would correspond to different length-breadth pairs that do not satisfy both perimeter 84 and difference 6 simultaneously.

Common Pitfalls:
Forgetting to divide perimeter by 2 to get L + B.Treating “6 m more” as L = 6B (incorrect).Multiplying wrong values or making arithmetic error in 24*18.Mixing up perimeter and area formulas.

Final Answer:
432 sq m