Problem:
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure , as shown. What is the perimeter of this region?
Answer Choices:
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B.
C.
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E.
Solution:
Since the square has side length , the diameter of each circular section is . The boundary of the region consists of semicircles, whose total perimeter is twice the circumference of a circle having diameter . Hence the perimeter of the region is
The problems on this page are the property of the MAA's American Mathematics Competitions