document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112309>Question 112309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 5 in. more than its width. Its area is 75 sq. in. what is the length and width 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 #81959 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that the area of a rectangle is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=lw ALIGN=MIDDLE  ALT=\"A=lw\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But the problem tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=w%2B5 ALIGN=MIDDLE  ALT=\"l=w%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The length (l) is (=) 5 in (5) more than (+) its width (w).\r<BR>\n" );
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document.write( "Since we know that the area is 75 sq. in., we can now write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B5%29%2Aw=75 ALIGN=MIDDLE  ALT=\"%28w%2B5%29%2Aw=75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying and solving:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B5w=75 ALIGN=MIDDLE  ALT=\"w%5E2%2B5w=75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B5w-75=0 ALIGN=MIDDLE  ALT=\"w%5E2%2B5w-75=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This one doesn't factor, so use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-5+%2B-+sqrt%28+5%5E2-4%28-75%29%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-5+%2B-+sqrt%28+5%5E2-4%28-75%29%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-5+%2B-+sqrt%28325%29%29%2F2 ALIGN=MIDDLE  ALT=\"w+=+%28-5+%2B-+sqrt%28325%29%29%2F2\"   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=w+=+%28-5+%2B-+5%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"w+=+%28-5+%2B-+5%2Asqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One of the possibilities, namely  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-5+-+5%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"w+=+%28-5+-+5%2Asqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, yields a negative result which is an absurdity when you are trying to find the length of a rectangle's side, therefore, the only valid answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-5+%2B+5%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"w+=+%28-5+%2B+5%2Asqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So now we have the width.\r<BR>\n" );
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document.write( "The length is just 5 inches longer, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+=+%28%28-5+%2B+5%2Asqrt%2813%29%29%2F2%29%2B5 ALIGN=MIDDLE  ALT=\"l+=+%28%28-5+%2B+5%2Asqrt%2813%29%29%2F2%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or in simpler terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=%285%2B5%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"l=%285%2B5%2Asqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Leave your answers in terms of these simplest form expressions containing the radicals.  If the problem had asked you to determine the length and width to some number of decimal places accuracy, THEN you would use a calculator and round appropriately, but you have to presume that exact expressions for the lengths are required because the problem asks \"what is the length and width\" without an accuracy specification. </SPAN>\n" );
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