document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78740>Question 78740</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131492578/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangular sign is 3 feet longer than the width.  If the sign's area is 54 square feet, find the length and the width.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56480 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem tells you that the Length (L) equals the Width (W) plus 3 feet. In equation <BR>\n" );
document.write( "form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+W+%2B+3 ALIGN=MIDDLE  ALT=\"L+=+W+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem also tells you that the Area (A) is 54 square feet.  From geometry you know that<BR>\n" );
document.write( "the formula for the Area of a rectangle is that Area equals the product of the Length<BR>\n" );
document.write( "times the Width.  In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+L%2AW+ ALIGN=MIDDLE  ALT=\"A+=+L%2AW+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute the given area to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+L%2AW ALIGN=MIDDLE  ALT=\"54+=+L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation has two unknowns. You can't solve it unless you can eliminate one of the<BR>\n" );
document.write( "unknowns. To do that you can note that L = W + 3.  If you substitute W + 3 for L in the<BR>\n" );
document.write( "equation you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+%28W+%2B+3%29%2AW ALIGN=MIDDLE  ALT=\"54+=+%28W+%2B+3%29%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And multiplying out the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+W%5E2+%2B+3W ALIGN=MIDDLE  ALT=\"54+=+W%5E2+%2B+3W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get this into the standard quadratic form by first subtracting 54 from both sides and<BR>\n" );
document.write( "then switching sides around to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+3W+-+54+=+0 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+3W+-+54+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This can be factored into:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2B9%29%2A%28W-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28W%2B9%29%2A%28W-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that this equation will be true if either of the 2 factors is a zero because<BR>\n" );
document.write( "zero times anything is zero and therefore equal to the right side of this equation.<BR>\n" );
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document.write( "Set W+9 equal to zero and solve to find that W = -9.  But what sense does a negative<BR>\n" );
document.write( "width make in this case?  None at all, so disregard this solution.<BR>\n" );
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document.write( "Next set W-6 equal to zero and solve to find that W = +6. That's better. The width is<BR>\n" );
document.write( "6 feet, and since we know that the length is 3 feet longer than the width, the length<BR>\n" );
document.write( "has to be 9 feet.  Check by noting that the product of the length times the width is<BR>\n" );
document.write( "9 ft times 6 ft and that equals the given area of 54 sq ft.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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