What is the perimeter of a semicircle? I. The radius of the semicircle equals half the side of a square. II. The area of the square is 196 sq cm.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:The goal is to compute a numeric perimeter for a semicircle. Conventionally, the perimeter of a semicircle includes the curved length plus the diameter: P = π*r + 2*r. We must see whether the given statements fix r uniquely. Given Data / Assumptions: I: r = (side of square)/2. II: Area of square = 196 sq cm ⇒ side = 14 cm. Concept / Approach:Use II to get the square’s side numerically; use I to link that side to r; then compute P = π*r + 2*r. Step-by-Step Solution: 1) From II: side s = √196 = 14 cm.2) From I: r = s/2 = 14/2 = 7 cm.3) Perimeter of semicircle: P = π*r + 2*r = 7π + 14 cm.4) Sufficiency: I alone gives only a relation; II alone gives only s. Together they yield a unique numeric answer. Verification / Alternative check:Some texts ask for curved length only (π*r); here “perimeter” explicitly includes the straight edge (diameter), which is standard for perimeter. Why Other Options Are Wrong: A/B/C/D: Neither I nor II alone is enough; together they are. Common Pitfalls:Omitting the diameter; misreading II as radius instead of side. Final Answer:Both statements together are sufficient, but NEITHER alone is sufficient.

What is the perimeter of a semicircle? I. The radius of the semicircle equals half the side of a square. II. The area of the square is 196 sq cm.

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