The difference between the length and breadth of a rectangle is 23 m, and its perimeter is 206 m. What is its area?

Problem restatementGiven L − B = 23 and perimeter 206, find L, B and hence area.

Given data

• L − B = 23
• 2(L + B) = 206 ⇒ L + B = 103

Concept/ApproachSolve the two linear equations for L and B, then multiply.

Step-by-Step calculationAdding: (L + B) + (L − B) = 103 + 23 ⇒ 2L = 126 ⇒ L = 63Then B = 103 − 63 = 40Area = 63 × 40 = 2,520 m²

Verification/AlternativeCheck: Perimeter = 2(63 + 40) = 206; difference = 23.

Common pitfallsDividing the perimeter by 2 at the wrong step or swapping L and B in the difference equation; either way, area is unchanged.

Final Answer2,520 m²