document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134122>Question 134122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a picture frame measures 34cm by 17cm. There is a 318cm^2 of picture showing. The frame is uniform thickness. Find the thickness of thr frame. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98090 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total area including the frames border is 34*17 or 578 cm^2\r<BR>\n" );
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document.write( "The area of the border alone is 578-318=260 cm^2\r<BR>\n" );
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document.write( "If you draw a picture, you may be able to follow what I'm doing\r<BR>\n" );
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document.write( "Area of the border=2(34*x)+2x(17-2x) and this equals\r<BR>\n" );
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document.write( "68x+34x -4x^2and we know that this equals 260 cm^2\r<BR>\n" );
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document.write( "-4x^2+102x-260=0  divide each term by -2<BR>\n" );
document.write( "2x^2-51x+130=0-------------------quadratic in standard form\r<BR>\n" );
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document.write( "Another way to arrive at this quadratic is to realize that the length and width of the picture that's showing is (34-2x) and (17-2x) and we know that \r<BR>\n" );
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document.write( "(34-2x)(17-2x)=318 expanding, using FOIL, we get:<BR>\n" );
document.write( "578-68x-34x+4x^2=318  subtract 318 from each side\r<BR>\n" );
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document.write( "578-318-102x+4x^2=318-318  collecting like terms<BR>\n" );
document.write( "260-102x+4x^2=0  divide each term by 2\r<BR>\n" );
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document.write( "2x^2-51x+130=0-----------quadratic in standard\r<BR>\n" );
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document.write( "Can you solve using the quadratic formula?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851+%2B-+sqrt%28+%28-51%29%5E2-4%2A2%2A130+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851+%2B-+sqrt%28+%28-51%29%5E2-4%2A2%2A130+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851+%2B-+sqrt%282601-1040+%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851+%2B-+sqrt%282601-1040+%29%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851+%2B-+sqrt%281561%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851+%2B-+sqrt%281561%29%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851+%2B-+39.509%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851+%2B-+39.509%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851+%2B39.509%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851+%2B39.509%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=22.627 ALIGN=MIDDLE  ALT=\"x=22.627\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm  DOESN'T WORK---LEADS TO NEGATIVE VALUE FOR AREA<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2851-+39.509%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2851-+39.509%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.872 ALIGN=MIDDLE  ALT=\"x=2.872\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "(34-2x)(17-2x)=318<BR>\n" );
document.write( "34-2*2.872)(17-2*2.872)=318<BR>\n" );
document.write( "28.255*11.256=318<BR>\n" );
document.write( "~~~~~~318=318\r<BR>\n" );
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document.write( "Hope this helps--ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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