Question 630501
The perimeter of a semicircle is doubled when the radius is increased by 3. Find the radius of the semicircle.
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perimeter of semicircle:
(pi)d/2 + d
in terms of r:
(pi)r/4 + 2r
r(pi/4 + 2)
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From: "perimeter of a semicircle is doubled when the radius is increased by 3" we get our equation:
2(r(pi/4 + 2)) = (r+3)(pi/4 + 2)
2(r(pi/4 + 2)) = 2(r+3)(pi/8 + 1)
r(pi/4 + 2) = (r+3)(pi/8 + 1)
r*pi/4 + 2r = rpi/8 + r + 3pi/8 +3
r*pi/4 + 2r -rpi/8 - r = 3pi/8 +3
r(pi/4 + 2 -pi/8 - 1) = 3pi/8 +3
r(pi/4 - pi/8 + 1) = 3pi/8 +3
r(2pi/8 - pi/8 + 1) = 3pi/8 +3
r(pi/8 + 1) = 3pi/8 +3
r(pi/8 + 1) = 3(pi/8 +1)
r = 3"