document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=780636>Question 780636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can not use algebra.\r<BR>\n" );
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document.write( "I painted a picture that is 4 inches longer than it is wide. If I put a 1 inch frame around my picture, the area increases by 48 square inches. What are the dimensions of my picture?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #475646 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=475646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You said, \"I can not use algebra.\"<BR>\n" );
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document.write( "Do you mean, you have too much difficulty trying to use algebra?  An analysis of the exercise can be shown and explained, and will use algebra.<BR>\n" );
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document.write( "Do you mean, the use of algebra is not permitted for this exercise?  That prohibition is unnacceptable; algebra is very well suited and is expected to this exercise.\r<BR>\n" );
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document.write( "Painted picture, w for width, y for length.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Bw. ALIGN=MIDDLE  ALT=\"y=4%2Bw.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Area for just the picture is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28wy=w%284%2Bw%29%29 ALIGN=MIDDLE  ALT=\"+highlight%28wy=w%284%2Bw%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1 inche frame extends length and width to be now<BR>\n" );
document.write( "width = w+1+1=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w%2B2%29 ALIGN=MIDDLE  ALT=\"highlight%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "length = y+1+1=(4+w)+1+1=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w%2B6%29 ALIGN=MIDDLE  ALT=\"highlight%28w%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Think about those distance size changes very carefully before continuing.  We add 2, not just 1.  We extend that 1 inch in TWO opposite directions, so that the 1 inche distance frame-width goes all the way around the picture.\r<BR>\n" );
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document.write( "The extended area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B2%29%28w%2B6%29 ALIGN=MIDDLE  ALT=\"%28w%2B2%29%28w%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Given is that the area increases by 48 square inches.  This means the difference between the two areas is 48 square inches.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28w%2B2%29%28w%2B6%29-w%284%2Bw%29=48%29 ALIGN=MIDDLE  ALT=\"highlight%28%28w%2B2%29%28w%2B6%29-w%284%2Bw%29=48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That appears to be a quadratic equation and just needs simplification.  Some help in starting through that is,...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B2w%2B6w%2B12-w%5E2-4w=48 ALIGN=MIDDLE  ALT=\"w%5E2%2B2w%2B6w%2B12-w%5E2-4w=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In fact this will not remain as a quadratic equation, since w^2-w^2=0.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8w-4w=48 ALIGN=MIDDLE  ALT=\"8w-4w=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w=48 ALIGN=MIDDLE  ALT=\"4w=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=12%29 ALIGN=MIDDLE  ALT=\"highlight%28w=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you can compute the y value yourself. </SPAN>\n" );
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