document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572708>Question 572708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 5 inches longer than the width. The area of the rectangle is 50 inches squared. Find the length and the 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 #368615 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First thing we want to do is write down what we know:\r<BR>\n" );
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document.write( "Area of a rectangle:<BR>\n" );
document.write( "A = L x W<BR>\n" );
document.write( "L = 5 + W  (length is 5 inches longer than the width)<BR>\n" );
document.write( "A = 50  (Area is 50 inches squared)\r<BR>\n" );
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document.write( "Putting this all together:<BR>\n" );
document.write( "L x W = 50<BR>\n" );
document.write( "Substituting for L with the above equation:<BR>\n" );
document.write( "(5+W) x W = 50<BR>\n" );
document.write( "Multiplying out the paren<BR>\n" );
document.write( "5W + W^2 = 50<BR>\n" );
document.write( "Subtract 50 from both sides and rearrange the terms a little:<BR>\n" );
document.write( "W^2 + 5W - 50 = 0\r<BR>\n" );
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document.write( "Now solve:<BR>\n" );
document.write( "(W _ _) (W _ _) = 0  (we need to figure out the operand and the term for each)<BR>\n" );
document.write( "The negative whole number indicates these have different signs<BR>\n" );
document.write( "(W - _) (W + _) = 0  <BR>\n" );
document.write( "We need to find two factors of 50 whose difference (subtract them) gives 5.<BR>\n" );
document.write( "50 = 25 x 2 Nope<BR>\n" );
document.write( "50 = 5 x 10 Yup!\r<BR>\n" );
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document.write( "Since the 5W term is positive, we need to put the 10 in the positive factor and 5 in the negative factor so ... <BR>\n" );
document.write( "(W - 5)(W + 10) = 0<BR>\n" );
document.write( "W -5 = 0<BR>\n" );
document.write( "W = 5<BR>\n" );
document.write( "W + 10 = 0<BR>\n" );
document.write( "W = -10\r<BR>\n" );
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document.write( "Since we're talking about the area of a rectangle, we have to assume it has positive sides or we've just entered another dimension.  :-)  So, <BR>\n" );
document.write( "W = 5 inches<BR>\n" );
document.write( "L = 5 + 5 (5 inches longer than the width)<BR>\n" );
document.write( "L = 10 inches\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "A = L x W<BR>\n" );
document.write( "A = 5 x 10<BR>\n" );
document.write( "50 = 50 Correct! </SPAN>\n" );
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