semi circulat region and square region have equal perimeter area of a square exceeds area of semicircular by 7 cm find the perimeter and area
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Expert's answer
2012-12-20T08:50:47-0500
Let a be side of square. Then square perimeter is 4a and square area is a^2Let r be radius of semicircle. Semicircular perimeter then is pi*r and semicircular area ispi*r^2 / 2 So we have4a=pi*r+2r = r(pi+2) (1) a^2 = pi*r^2 / 2 + 7 (2)
from (1) we find a = (pi+2)*r/4 substituting to (2) gives (pi+2)^2 r^2 / 16 = pi* r^2 / 2 + 7 (pi+2)^2 / 8 * r^2 = pi * r^2 + 14 ((pi^2+4pi+4)/8 - pi) r^2 = 14 0.1629 r^2 = 14 r = 9.27 hence perimeter of semicircle and square is 47.66 area of square is 141.97 are of circle is 134.97
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