document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924758>Question 924758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wire is bent into a square enclosing an Area of 48cm^2. If it is to be reshaped as an equilateral triangle, how much araea will be lost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561069 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=561069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2848%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perimeter, or the length of the wire.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%2A4%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%2A4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2A4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2816%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%2816%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the wire length.\r<BR>\n" );
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document.write( "The equilateral triangle formed with that length of wire is of side length and base length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F3%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"%2816%2F3%29sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is also then the hypotenuse of a special 30-60-90 triangle.  You can consider <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2816%2F3%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2816%2F3%29sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be the short leg of a 30-60-90 triangle; The height of the equilateral triangle, being the other leg of the special 30-60-90, can be called y.\r<BR>\n" );
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document.write( "This y is found, using Pythagorean Theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B%28%288%2F3%29sqrt%283%29%292=%28%2816%2F3%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"y%5E2%2B%28%288%2F3%29sqrt%283%29%292=%28%2816%2F3%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Find the area of the equilateral triangle from base and height y.\r<BR>\n" );
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document.write( "Continuing for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B%288%2F3%29%5E2%2A3=%2816%2F3%29%5E2%2A3 ALIGN=MIDDLE  ALT=\"y%5E2%2B%288%2F3%29%5E2%2A3=%2816%2F3%29%5E2%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=3%2816%2F3%29%5E2-3%288%2F3%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2=3%2816%2F3%29%5E2-3%288%2F3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=%2816%29%5E2%2F3-64%2F3 ALIGN=MIDDLE  ALT=\"y%5E2=%2816%29%5E2%2F3-64%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=192%2F3 ALIGN=MIDDLE  ALT=\"y%5E2=192%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=%283%2A64%29%2F3 ALIGN=MIDDLE  ALT=\"y%5E2=%283%2A64%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=64 ALIGN=MIDDLE  ALT=\"y%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=8%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area OF the equilateral triangle here is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%2816%2F3%29sqrt%283%29%29%288%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28%2816%2F3%29sqrt%283%29%29%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is half of base*times*height.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2816%2F3%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2816%2F3%29sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%2864%2F3%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%2864%2F3%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The question asks for the difference or how much area is lost in forming the triangle, so you want to find  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2848-%2864%2F3%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight%2848-%2864%2F3%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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