document.write( "Question 58255: A semicircle is placed on one side of a square so that its diameter coincides with a side of the square. Find the side length of the square if the total area of the square plus the semicircle is 200 square inches. \n" ); document.write( "
Algebra.Com's Answer #39974 by ankor@dixie-net.com(22740)\"\" \"About 
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A semicircle is placed on one side of a square so that it's diameter coincides with a side of the square. Find the side length of the square if the total area of the square plus the semicircle is 200 square inches.
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\n" ); document.write( "Let x = one side & diamter of the semicircle
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\n" ); document.write( "Square area + semicircle area = 200
\n" ); document.write( "Radius = .5x
\n" ); document.write( "x^2 + (pi(.5x)^2)/2 = 200
\n" ); document.write( "x^2 + (pi*.25x^2)/2 = 200
\n" ); document.write( "2x^2 + pi*.25x^2 = 400; multiplied eq by 2
\n" ); document.write( "2x^2 + .785x^2 = 400
\n" ); document.write( "2.785x^2 = 400
\n" ); document.write( "x^2 = 400/2.785
\n" ); document.write( "x^2 = 143.6
\n" ); document.write( "x = SqRt[143.6]
\n" ); document.write( "x = 11.98 ~ 12 inches:\r
\n" ); document.write( "\n" ); document.write( "Check: r = 6 inches; 144 + (pi*36)/2 = 200.55 ~ 200
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