Question 333037
Let P =the perimeter of semicircle
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P = Circumference/2 + Diameter
{{{P = (2*pi*r)/2 + 2*r}}}
{{{P = pi*r +2*r}}}
{{{P = r*(pi +2)}}}
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You are given:  perimeter of semicircle = area of semicircle
{{{perimeter of semicircle =r*(pi +2)  = Area of semicircle= (pi*r^2)/2 }}}
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{{{r*(pi +2)  = (pi*r^2)/2 }}}
{{{2*r*(pi+2)=pi*r^2}}}   (multiply both sides by 2)
{{{2*(pi+2)=pi*r}}}        (divide both sides by r)
{{{2*(pi+2)/pi=r}}}       (divide both sides by {{{pi}}})
{{{2*(pi+2)/pi=2*(pi/pi)+4/pi=2+4/pi=r}}}