document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=559691>Question 559691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Karina has a piece of wire that is 16 inches long. Use this fact to answer the following questions. Round your answers to the nearest tenth.\r<BR>\n" );
document.write( "\n" );
document.write( "a. What will be the area inside a semicircle made from this wire?\r<BR>\n" );
document.write( "\n" );
document.write( "c. Suppose that Karina cuts the wire into 2 pieces to make 2 squares such that the area of 1 square is twice the area of the other. What is the side length of the larger square?\r<BR>\n" );
document.write( "\n" );
document.write( "thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363498 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Karina has a piece of wire that is 16 inches long. Use this fact to answer the following questions. Round your answers to the nearest tenth. <BR>\n" );
document.write( "a. What will be the area inside a semicircle made from this wire?<BR>\n" );
document.write( "Perimeter = (pi)d = 16 inches<BR>\n" );
document.write( "d = 16/(pi)<BR>\n" );
document.write( "radius = 8/(pi)<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "Area = (pi)[8/(pi)]^2<BR>\n" );
document.write( "Area = 64/(pi) sq. inches<BR>\n" );
document.write( "================================================= <BR>\n" );
document.write( "c. Suppose that Karina cuts the wire into 2 pieces to make 2 squares such that the area of 1 square is twice the area of the other. What is the side length of the larger square?<BR>\n" );
document.write( "Let one piece be \"x\":<BR>\n" );
document.write( "Other piece is \"16-x\"<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Areas:<BR>\n" );
document.write( "1st square<BR>\n" );
document.write( "side = x/4<BR>\n" );
document.write( "Area = (x/4)^2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2nd square:<BR>\n" );
document.write( "side = (16-x)/4<BR>\n" );
document.write( "Area = [(16-x)/4]^2<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "Area #1 = 2 Area #2<BR>\n" );
document.write( "(x/4)^2 = 2[(16-x)/4]^2<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Multiply both sides by 16:<BR>\n" );
document.write( "x^2 = 2(16-x)^2<BR>\n" );
document.write( "x^2 = 2(256 - 32x + x^2)<BR>\n" );
document.write( "x^2 = 512 - 64x + 2x^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 - 64x +512 = 0<BR>\n" );
document.write( "I graphed it to get x = 9.37 and x = 54.63<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===========================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "thanks! <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );