1982 AHSME Problems/Problem 4
Revision as of 14:57, 23 July 2022 by Firedragonmath16 (talk | contribs)
Problem
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
Solution
by mathhayden (bad)
perimeter=2r+pi2r=2r(pi+1)
area=[pi(r^2)]/2
make them equal & solve for r: pi(r^2)/2=2r(pi+1) pi(r^2)=4r(pi+1) (r^2)=4r[(pi+1)/pi] r=4(pi+1)/pi
=Ans.