Rectangle — Difference of sides is 23 m and perimeter is 206 m. Find its area.

Introduction / Context:With the perimeter and the difference of sides known, one can reconstruct the two sides by solving simultaneous linear equations, then compute the area as the product of the two sides.

Given Data / Assumptions:

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

Concept / Approach:Sum and difference determine the values: L = ( (L + B) + (L − B) ) / 2; B = ( (L + B) − (L − B) ) / 2.

Step-by-Step Solution:L = (103 + 23) / 2 = 63B = (103 − 23) / 2 = 40Area = L * B = 63 * 40 = 2520 m2

Verification / Alternative check:Perimeter check: 2(63 + 40) = 206 ✔; difference 63 − 40 = 23 ✔

Why Other Options Are Wrong:2480 and 2420 come from arithmetic slips; “None” is incorrect because 2520 m2 fits perfectly.

Common Pitfalls:Dividing perimeter by 2 twice or mixing up sum/difference formulas.

Final Answer:2520 m2