document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133761>Question 1133761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the lengths of the two equal sides of an isosceles triangle are each x cm, find the length for the third side so that the triangle has maximum area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751013 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the lengths of the two equal sides of an isosceles triangle are each x cm, find the length for the third side so that the triangle has maximum area.<BR>\n" );
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document.write( "The 3rd side's length is 2s.<BR>\n" );
document.write( "Area = b*h/2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+sqrt%28x%5E2+-+s%5E2%29 ALIGN=MIDDLE  ALT=\"h+=+sqrt%28x%5E2+-+s%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=Area+A+=+s%2Asqrt%28x%5E2+-+s%5E2%29+=+%28s%5E2%2Ax%5E2+-+s%5E4%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"Area+A+=+s%2Asqrt%28x%5E2+-+s%5E2%29+=+%28s%5E2%2Ax%5E2+-+s%5E4%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fds+=+%281%2F2%29%2A%28s%5E2%2Ax%5E2+-+s%5E4%29%5E%28-1%2F2%29%2A%282s%2Ax%5E2+-+4s%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fds+=+%28s%5E2%2Ax%5E2+-+s%5E4%29%5E%28-1%2F2%29%2A%28s%2Ax%5E2+-+2s%5E3%29 ALIGN=MIDDLE  ALT=\"dA%2Fds+=+%28s%5E2%2Ax%5E2+-+s%5E4%29%5E%28-1%2F2%29%2A%28s%2Ax%5E2+-+2s%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find s for dA/ds = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2Ax%5E2+-+2s%5E3+=+0 ALIGN=MIDDLE  ALT=\"s%2Ax%5E2+-+2s%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Ignore s = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2s%5E2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+2s%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = x*sqrt(2)/2<BR>\n" );
document.write( "Side length = x*sqrt(2)<BR>\n" );
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document.write( "Might be a lot simpler to assign a number to x, eg, 10.<BR>\n" );
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document.write( "The other tutor assumed it's a right triangle, which it is, but he showed no proof of it.<BR>\n" );
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document.write( "I would have guessed that the equilateral triangle would give the max area.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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