document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641565>Question 641565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The width of a rectangle is 8m less them the length. The area is 308^2m. Solve for width and the length.<BR>\n" );
document.write( "Please help<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403721 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=403721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve, let's change the first two sentences into equations.  The first sentence says that the width of a rectangle is 8m less than the length.  In other words,\r<BR>\n" );
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document.write( "W = L - 8\r<BR>\n" );
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document.write( "The second sentence says that the area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=308m%5E2 ALIGN=MIDDLE  ALT=\"308m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The area of a rectangle is L x W (length times width).  So, in our second sentence, our equation would be\r<BR>\n" );
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document.write( "L x W = 308\r<BR>\n" );
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document.write( "Now, substitute L - 8 for the W in the second equation, and we will find our length:\r<BR>\n" );
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document.write( "L x (L - 8) = 308\r<BR>\n" );
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document.write( "Using the distributive property of multiplication, multiply L by (L - 8), which will give us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+8L+=+308 ALIGN=MIDDLE  ALT=\"L%5E2+-+8L+=+308\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we subtract 308 from both sides of the equal sign, we will have a quadratic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+-+8L+-+308+=+0 ALIGN=MIDDLE  ALT=\"L%5E2+-+8L+-+308+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can now solve for L by factoring, completing the square, or by using the quadratic formula.  Factoring is the easiest, so let's see if there are two numbers that when multiplied give us -308, and when added, give us -8:\r<BR>\n" );
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document.write( "1 x -308 = -308; 1 + -308 = -307  this won't work<BR>\n" );
document.write( "-1 x 308 = -308; -1 + 308 = 307  this won't work\r<BR>\n" );
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document.write( "Let's try some bigger numbers.  How about 14 and 22?\r<BR>\n" );
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document.write( "-14 x 22 = -308; -14 + 22 = 8  this won't work<BR>\n" );
document.write( "14 x -22 = -308; 14 + -22 = -8  this works!\r<BR>\n" );
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document.write( "We see that 14 and -22 work, so:\r<BR>\n" );
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document.write( "(L + 14)(L - 22) = -308, so\r<BR>\n" );
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document.write( "L = -14 and L = 22\r<BR>\n" );
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document.write( "Now, the length of a rectangle can never be a negative number, so -14 cannot be our length.  So, our length must be 22 meters\r<BR>\n" );
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document.write( "We know from the first sentence in our problem, that the width is 8m less than the length.  Since the length is 22, our width will be 8 less than that:\r<BR>\n" );
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document.write( "22 - 8 = 14\r<BR>\n" );
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document.write( "So, our width is 14m\r<BR>\n" );
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document.write( "FINAL ANSWER:  Length = 22m  and Width = 14m </SPAN>\n" );
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