document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194518>Question 1194518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular painting is to have a total area (including the frame)<BR>\n" );
document.write( "of 1200 cm2. If the painting is 30 cm long and 20 cm wide, find<BR>\n" );
document.write( "the width of the frame. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826728 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = width of the frame in centimeters.<BR>\n" );
document.write( "This is some positive real number, meaning that x > 0\r<BR>\n" );
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document.write( "The width of 30 cm bumps up to 30+x+x = 30+2x cm<BR>\n" );
document.write( "This is because we add on two copies of x for either side along the 30 cm dimension.<BR>\n" );
document.write( "The same thing happens with the 20 cm bumping up to 20+2x cm.\r<BR>\n" );
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document.write( "The painting + frame has dimensions of (30+2x) cm by (20+2x) cm\r<BR>\n" );
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document.write( "Multiply those dimensions and set the product equal to the stated total area of 1200 sq cm.\r<BR>\n" );
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document.write( "length*width = area<BR>\n" );
document.write( "(30+2x)*(20+2x) = 1200<BR>\n" );
document.write( "600+60x+40x+4x^2 = 1200<BR>\n" );
document.write( "600+100x+4x^2 = 1200<BR>\n" );
document.write( "4x^2+100x+600-1200 = 0<BR>\n" );
document.write( "4x^2+100x-600 = 0<BR>\n" );
document.write( "4(x^2+25x-150) = 0<BR>\n" );
document.write( "x^2+25x-150 = 0/4<BR>\n" );
document.write( "x^2+25x-150 = 0\r<BR>\n" );
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document.write( "Now use the quadratic formula to find x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   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=x+=+%28-%2825%29%2B-sqrt%28%2825%29%5E2-4%281%29%28-150%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2825%29%2B-sqrt%28%2825%29%5E2-4%281%29%28-150%29%29%29%2F%282%281%29%29\"   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=x+=+%28-25%2B-sqrt%281225%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-25%2B-sqrt%281225%29%29%2F%282%29\"   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=x+=+%28-25%2B-++35%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-25%2B-++35%29%2F%282%29\"   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=x+=+%28-25%2B35%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-25%2B35%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-25-35%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-25-35%29%2F%282%29\"   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=x+=+%2810%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-60%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-60%29%2F%282%29\"   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=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ignore the negative solution. Recall at the top we stated that x > 0.\r<BR>\n" );
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document.write( "Answer: The width of the frame is 5 cm.<BR>\n" );
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