document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190852>Question 1190852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the outside of a picture frame has a length which is 5cm more than the width, the area enclosed of the picture frame is 126cm what is the width of the outside </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822598 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "An attempt to solve the problem using formal algebra leads to this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B5%29=126 ALIGN=MIDDLE  ALT=\"x%28x%2B5%29=126\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x=126 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x=126\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-126=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-126=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To solve that by factoring, you need to find two integers whose product is 126 and whose difference is 5.  But that is what the original problem asks you to do, so the formal algebra doesn't get you any closer to the answer.<br><BR>\n" );
document.write( "So if formal algebra is required and you aren't going to finish the solution by finding two integers whose product is 126 and whose difference is 5, then you have to use the quadratic formula; and that is just plugging numbers into a formula, which doesn't teach you anything or give you any mental exercise.<br><BR>\n" );
document.write( "So do what the other tutor says: just find the two integers whose product is 126 and whose difference is 5.  Do that by looking at all the pairs of integers with a product of 126:<br><BR>\n" );
document.write( "126 = 126 * 1<BR>\n" );
document.write( "126 =  63 * 2<BR>\n" );
document.write( "126 =  42 * 3<BR>\n" );
document.write( "126 =  21 * 6<BR>\n" );
document.write( "126 =  14 * 9 <-- there it is<br><BR>\n" );
document.write( "ANSWER: width 9 (and length 14)<br><BR>\n" );
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