document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637975>Question 637975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The width of a rectangle is two less than its length. If the area of the rectangle is 42, what is the length of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401985 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to solve this problem, first find the given.  In this case, it tells you that the width is 2 less than the length.  In other words, W=L-2.  Since the question involves the area of a rectangle, we will need to use the formula for finding the area of a rectangle, which is A=L X W, where L is length and W is width.  So, let's set up our two equations:\r<BR>\n" );
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document.write( "W=L - 2<BR>\n" );
document.write( "42=L X W\r<BR>\n" );
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document.write( "We can substitute L - 2 for the W in the second equation.  So, we would have\r<BR>\n" );
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document.write( "42 = L X (L-2) or L(L-2)\r<BR>\n" );
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document.write( "We would multiply the L-2 by L, which is L^2-2L, so we now have\r<BR>\n" );
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document.write( "42 = L^2 - 2L\r<BR>\n" );
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document.write( "When we subtract 42 from both sides of our equation, we see that we are left with a linear equation:\r<BR>\n" );
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document.write( "L^2 - 2L - 42 = 0\r<BR>\n" );
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document.write( "So, to solve for L (the length), use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%2B1%2A-42%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%2B1%2A-42%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2B-sqrt%284%2B168%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%284%2B168%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=%282%2B-sqrt%28172%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%28172%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=%282%2B-sqrt%284%2A43%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%284%2A43%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=%282%2B-2sqrt%2843%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-2sqrt%2843%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=%281%2B-sqrt%2843%29%29 ALIGN=MIDDLE  ALT=\"x=%281%2B-sqrt%2843%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the length of our rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"1%2B-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that the width of our rectangle 2 less than our length, so the width would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B-sqrt%2843%29-2 ALIGN=MIDDLE  ALT=\"1%2B-sqrt%2843%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"-1%2B-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Length = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"1%2B-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Width = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"-1%2B-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, neither the length nor the width of a rectangle can be a negative number.  So, our length cannot be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"1-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because that is a negative number.  Similarly, our width cannot be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1-sqrt%2843%29 ALIGN=MIDDLE  ALT=\"-1-sqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because that too is a negative number.  So, our final answer would be:\r<BR>\n" );
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document.write( "Length = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%2843%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Width = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Bsqrt%2843%29 ALIGN=MIDDLE  ALT=\"-1%2Bsqrt%2843%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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