Square from twice the rectangle’s perimeter; semicircle with diameter equal to the square’s side: A rectangle has dimensions 8 cm by 7 cm. A square has perimeter equal to twice the rectangle’s perimeter. Find the perimeter of the semicircle (curved arc + diameter) whose diameter equals the side of that square.

Introduction / Context:Convert a rectangle’s perimeter to a square’s perimeter to deduce the square’s side. Then compute a semicircle’s perimeter when its diameter equals that side.

Given Data / Assumptions:

• Rectangle: 8 cm by 7 cm ⇒ perimeter P_rect = 2(8+7) = 30 cm.
• Square perimeter = 2 * P_rect = 60 cm ⇒ side s = 60/4 = 15 cm.
• Semicircle with diameter d = s = 15 cm.

Concept / Approach:Perimeter of a semicircle (including the straight diameter) = (πd)/2 + d.

Step-by-Step Solution:

Verification / Alternative check:Using π ≈ 22/7 yields 38.571… cm, matching the option.

Why Other Options Are Wrong:They correspond to using only the arc or incorrect substitutions for d.

Common Pitfalls:Confusing “circumference of semicircle” with arc-only; here perimeter explicitly includes the diameter.

Final Answer:38.57 cm.