document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995807>Question 995807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need some explanation on how this is solved.\r<BR>\n" );
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document.write( "An isosceles triangle has base 7 and height 14. Find the maximum possible area of a rectangle that can be placed inside the triangle with one side on the base of the triangle. (Hint: Similar triangles may be of assistance.) \r<BR>\n" );
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document.write( "Area[max] = \r<BR>\n" );
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document.write( "I had help on solving this but was confused by the answer. I know that an isosceles triangle is one with two equal sides. What I am confused on how this answer was derived. What exactly is happening here? how are \"compare ratios\" being implemented et cetera\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2F2%29%2F+%287%2F2%29+ ALIGN=MIDDLE  ALT=\"+%28x%2F2%29%2F+%287%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2814-y%29%2F+14+ ALIGN=MIDDLE  ALT=\"+%2814-y%29%2F+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+14-2x+ ALIGN=MIDDLE  ALT=\"+y+=+14-2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AREA+=+xy+=+14x-2x%5E2+ ALIGN=MIDDLE  ALT=\"+AREA+=+xy+=+14x-2x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+For+maxm+area+ ALIGN=MIDDLE  ALT=\"+For+maxm+area+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dA%2Fdx=0+ ALIGN=MIDDLE  ALT=\"+dA%2Fdx=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14-4x=0+ ALIGN=MIDDLE  ALT=\"+14-4x=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=3.5+ ALIGN=MIDDLE  ALT=\"+x=3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+7+ ALIGN=MIDDLE  ALT=\"+y=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MaxArea+=+7+x+3.5+ ALIGN=MIDDLE  ALT=\"+MaxArea+=+7+x+3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MaxArea+=+24.5+square+units+ ALIGN=MIDDLE  ALT=\"+MaxArea+=+24.5+square+units+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Please could someone explain what is happening in each step here. I have no idea how this answer was formed.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614501 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=614501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An isosceles triangle has base 7 and height 14. Find the maximum possible area of a rectangle that can be placed inside the triangle with one side on the base of the triangle. (Hint: Similar triangles may be of assistance.) \r<BR>\n" );
document.write( "\n" );
document.write( "Area[max] = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I had help on solving this but was confused by the answer. I know that an isosceles triangle is one with two equal sides. What I am confused on how this answer was derived. What exactly is happening here? how are \"compare ratios\" being implemented et cetera\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2F2%29%2F+%287%2F2%29+ ALIGN=MIDDLE  ALT=\"+%28x%2F2%29%2F+%287%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2814-y%29%2F+14+ ALIGN=MIDDLE  ALT=\"+%2814-y%29%2F+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+14-2x+ ALIGN=MIDDLE  ALT=\"+y+=+14-2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AREA+=+xy+=+14x-2x%5E2+ ALIGN=MIDDLE  ALT=\"+AREA+=+xy+=+14x-2x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+For+maxm+area+ ALIGN=MIDDLE  ALT=\"+For+maxm+area+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dA%2Fdx=0+ ALIGN=MIDDLE  ALT=\"+dA%2Fdx=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14-4x=0+ ALIGN=MIDDLE  ALT=\"+14-4x=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=3.5+ ALIGN=MIDDLE  ALT=\"+x=3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+7+ ALIGN=MIDDLE  ALT=\"+y=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MaxArea+=+7+x+3.5+ ALIGN=MIDDLE  ALT=\"+MaxArea+=+7+x+3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MaxArea+=+24.5+square+units+ ALIGN=MIDDLE  ALT=\"+MaxArea+=+24.5+square+units+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Please could someone explain what is happening in each step here. I have no idea how this answer was formed.\r<BR>\n" );
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document.write( "Sketch a rectangle INSIDE an isoscles triangle.<BR>\n" );
document.write( "Let the rectangle width = x and the rectangle height be y<BR>\n" );
document.write( "Sketch the perpendicular hisector of the isosceles<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Notice the upper triangle inside the original triangle.<BR>\n" );
document.write( "Notice that the upper triangle has two identical halfs.<BR>\n" );
document.write( "Notice that one of those halfs is proportional to half of the isosceles triangle.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Proportion:<BR>\n" );
document.write( "base/base = height/height<BR>\n" );
document.write( "(x/2)/(7/2) = (14-y)/y<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Your tutor worked with this proportion to find<BR>\n" );
document.write( "and x and y that would give the dimensions of<BR>\n" );
document.write( "the rectangle with the maximum area.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------- </SPAN>\n" );
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