1982 AMC 12 Problem 4
Attempt Problem 4 of the 1982 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1982 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
The perimeter of a semicircular region, measured in centimeters, is numerically equal to its area, measured in square centimeters. The radius of the semicircle, measured in centimeters, is
Answer: E
Small hint:
Include the diameter in the perimeter of the region
Big hint:
Set equal to
Solution:
For equality of perimeter and area gives Dividing by and solving yields
Therefore, the correct answer is E.
Problem 4 in other years
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