document.write( "Question 223686: a square and a semicurcular region have the same perimeter. If the length of the radius of the semicirular region is 8 what is the length of a side of a square? \n" ); document.write( "
Algebra.Com's Answer #167186 by rapaljer(4671)\"\" \"About 
You can put this solution on YOUR website!
If the radius of the semicircle is 8, then the circumference of the entire circle is \"C=2%2Api%2Ar=2%2Api%2A8\". \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since it's a semicircle, take half of this, and add in a diameter of 16, and you get the perimeter of the semicircle is \"pi%2A8%2B16\" \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let x = side of the square, which has a perimeter of 4x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the perimeter of the square equals the perimeter of the semicircle,
\n" ); document.write( "\"4x=8%2Api%2B16\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Divide both sides by 4:
\n" ); document.write( "\"x=2%2Api+%2B4\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "R^2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Dr. Robert J. Rapalje, Retired
\n" ); document.write( "Seminole State College of Florida
\n" ); document.write( "Altamonte Springs Campus\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );