document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176144>Question 1176144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Heart modeled with a square and two semi-circles. You use red for the square and lighter red for the semi circles. the problem is you only have enough red for a perimeter of 120cm per figure. If you maximize the squares what will be the area of the heart. \r<BR>\n" );
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document.write( "I think this is a quadratic but I am not sure any insight would be appreciated </SPAN>\n" );
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document.write( "I will guess that the \"heart\" is a square with two semicircles of the same radius on the top edge of the square....<br><BR>\n" );
document.write( "Let x be the radius of each of the semicircles; then the side length of the square is 4x.<br><BR>\n" );
document.write( "The perimeter of the heart is then the length of 3 sides of the square plus the circumferences of the two semicircles -- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284x%29%2B2%28pi%29%28x%29+=+x%2812%2B2pi%29 ALIGN=MIDDLE  ALT=\"3%284x%29%2B2%28pi%29%28x%29+=+x%2812%2B2pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The maximum perimeter is 120cm:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2812%2B2pi%29+=+120 ALIGN=MIDDLE  ALT=\"x%2812%2B2pi%29+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+120%2F%2812%2B2pi%29 ALIGN=MIDDLE  ALT=\"x+=+120%2F%2812%2B2pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use a calculator to find the value of x.<br><BR>\n" );
document.write( "The area of the heart is the area of the square, plus the area of the two semicircles; the two semicircles together make a full circle.<br><BR>\n" );
document.write( "The area of the heart is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%29%5E2+%2B+%28pi%29x%5E2 ALIGN=MIDDLE  ALT=\"%284x%29%5E2+%2B+%28pi%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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