document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826261>Question 826261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the area of a rectangle is 270cm^2. If the shorter side was reduced by 2cm and the longer side was increased by 16 cm^2. Find the lengths of the sides of the original rectangle.<BR>\n" );
document.write( "Note the book says 16cm^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497982 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39616)</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=497982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The book is wrong.  The item should go this way:\r<BR>\n" );
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document.write( "\"The area of a rectangle is 270cm^2. If the shorter side was reduced by 2cm and the longer side was increased by 16 CM, find the lengths of the sides of the original rectangle.\"\r<BR>\n" );
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document.write( "So you have two lengths, x and y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=270%2Acm%5E2 ALIGN=MIDDLE  ALT=\"xy=270%2Acm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Then the IF part, x-2 for one length, and y+16 for the other length.  \"Find the lengths\" or values of x and y.\r<BR>\n" );
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document.write( "That is, what is (x-2)(y+16) and how does it compare to xy=270?  The item still seems missing something.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28y%2B16%29=xy-2y%2B16x-32=270-2y%2B16x-32=highlight_green%2816x-2y%2B238%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28y%2B16%29=xy-2y%2B16x-32=270-2y%2B16x-32=highlight_green%2816x-2y%2B238%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, STILL A VARIABLE EXPRESSION.  What is it supposed to be equal to?  Not given. Not described enough.\r<BR>\n" );
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document.write( "That is as far as can be done!  (See \"Further Thought\").\r<BR>\n" );
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document.write( "-------------Further Thought-------------\r<BR>\n" );
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document.write( "Along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=270 ALIGN=MIDDLE  ALT=\"xy=270\"   DISABLED_style= \"max-width:90%; height:auto;\" >, also is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x-2y%2B238%3E0 ALIGN=MIDDLE  ALT=\"16x-2y%2B238%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Working with these,<BR>\n" );
document.write( "y=270/x and 8x-y+119>0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C8x%2B119 ALIGN=MIDDLE  ALT=\"y%3C8x%2B119\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and substituting for y, obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2Fx%3C8x%2B119 ALIGN=MIDDLE  ALT=\"270%2Fx%3C8x%2B119\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We expect that x>0, so if multiply both sides by x, we have no change in order relation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%3C8x%5E2%2B119x ALIGN=MIDDLE  ALT=\"270%3C8x%5E2%2B119x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C8x%5E2%2B119x-270 ALIGN=MIDDLE  ALT=\"0%3C8x%5E2%2B119x-270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288x%5E2%2B119x-270%3E0%29 ALIGN=MIDDLE  ALT=\"highlight%288x%5E2%2B119x-270%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which we CAN work with.<BR>\n" );
document.write( "'<BR>\n" );
document.write( "x critical points are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-119%2Bsqrt%28119%5E2-4%2A8%2A%28-270%29%29%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%28-119%2Bsqrt%28119%5E2-4%2A8%2A%28-270%29%29%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-119-sqrt%28119%5E2-4%2A8%2A%28-270%29%29%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"%28-119-sqrt%28119%5E2-4%2A8%2A%28-270%29%29%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Discriminant is 22801.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2822801=151%5E2%29 ALIGN=MIDDLE  ALT=\"highlight_green%2822801=151%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then the critical points, x are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-119%2B151%29%2F16 ALIGN=MIDDLE  ALT=\"%28-119%2B151%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-119-151%29%2F16 ALIGN=MIDDLE  ALT=\"%28-119-151%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, only the positive one making sense for the problem.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E%28151-119%29%2F16%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E%28151-119%29%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Still unfinished for y, but maybe you could finish this. </SPAN>\n" );
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