document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572611>Question 572611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 2 feet more than 3 times the width. If the area is 16 square feet, find the width and the length. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368616 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=368616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let's write down everything we know:<BR>\n" );
document.write( "L = 2 + 3W  (length is 2 feet more than 3 times the width)<BR>\n" );
document.write( "A is 16 sq ft<BR>\n" );
document.write( "A = L x W\r<BR>\n" );
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document.write( "If we substitute in the area formula so we only have one variable, W:<BR>\n" );
document.write( "L x W = 16<BR>\n" );
document.write( "(2+3W) x W = 16  Multiplying out the paren<BR>\n" );
document.write( "2W + 3W^2 = 16<BR>\n" );
document.write( "Let's rearrange the terms:<BR>\n" );
document.write( "3W^2 + 2W = 16  <BR>\n" );
document.write( "Subtracting 16 from each side:<BR>\n" );
document.write( "3W^2 + 2W - 16 = 0\r<BR>\n" );
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document.write( "Now we factor this:<BR>\n" );
document.write( "(3W _ _) (W _ _) = 0  Where we have to figure out the operators and terms<BR>\n" );
document.write( "What are factors of 16 that we can try?<BR>\n" );
document.write( "16 = 4x4<BR>\n" );
document.write( "16 = 8x2 (oh good, there's only 2)\r<BR>\n" );
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document.write( "Let's try the 2 4s:<BR>\n" );
document.write( "(3W _ 4)(W _ 4) = 0<BR>\n" );
document.write( "Since 16 is negative, one must be positive, the other negative:<BR>\n" );
document.write( "Try:<BR>\n" );
document.write( "(3W - 4)(W + 4) = 3W^2 + 12W - 4W -16    (12-4 is not 2 so this isn't it)<BR>\n" );
document.write( "Try:<BR>\n" );
document.write( "(3W - 2)(W + 8) = 3W^2 + 24W - 2W -16    (24-2 is not 2 so let's switch the 2 & 8 and try this one again)<BR>\n" );
document.write( "(3W - 8)(W + 2) = 3W^2 + 6W - 8W - 16    (6-8 is neg 2 so let's switch the signs)<BR>\n" );
document.write( "(3W + 8)(W - 2) = 3W^2 -6W + 8W -16 <BR>\n" );
document.write( "= 3W^2 + 2W -16  Yay!<BR>\n" );
document.write( "Writing it again so we can finish:<BR>\n" );
document.write( "(3W + 8)(W-2) = 0<BR>\n" );
document.write( "3W + 8 = 0 Subtract 8 from both sides:<BR>\n" );
document.write( "3W = -8  Divide both sides by 3<BR>\n" );
document.write( "W = -8/3  (not likely since this is a rectangle that the width is negative)<BR>\n" );
document.write( "W - 2 = 0  Add 2 to both sides<BR>\n" );
document.write( "W = 2 Aha!\r<BR>\n" );
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document.write( "Now we need to figure the length:<BR>\n" );
document.write( "L = 2+3xW<BR>\n" );
document.write( "L = 2+3(2)<BR>\n" );
document.write( "L = 2+6<BR>\n" );
document.write( "L = 8\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "A = L x W<BR>\n" );
document.write( "A = 8 x 2<BR>\n" );
document.write( "16 = 16 Correct!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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