Rectangle — Length 20 cm, Area 200 cm^2; Area Increased by 1 1/5 Times by Increasing Length Only: Find the new perimeter (in cm).

Introduction / Context:The problem states the area is increased by “1 1/5 times” the original by changing length only. In standard wording, “increased by 1 1/5 times” means the increase equals 1.2 of the original, so the new area becomes 1 + 1.2 = 2.2 times. However, many aptitude items intend “becomes 1 1/5 times,” i.e., 1.2 times. We apply the Recovery-First policy and adopt the widely used interpretation: new area = 1.2 * original, since the answer options align with this reading.

Given Data / Assumptions:

• Original: L = 20 cm, A = 200 cm^2 ⇒ B = A/L = 10 cm
• Only L changes; B fixed at 10 cm
• New area A' = 1.2 * 200 = 240 cm^2 (assumed per standard aptitude phrasing)

Concept / Approach:With breadth fixed, new length L' = A' / B. Compute perimeter P' = 2(L' + B). This directly uses rectangle area and perimeter definitions under the clarified assumption.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 60, 64, 72, 76 come from misreading the phrase or changing breadth too.

Common Pitfalls:

• Linguistic ambiguity in “increased by x times.” Always reconcile with options.

Final Answer:68.