document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77419>Question 77419</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Geometry. The area of a rectangle of length x is given by 3x^2 + 5x. Find 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 #55544 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=55544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle of length x is given by 3x^2 + 5x. Find the width of the rectangle.<BR>\n" );
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document.write( "The area of a rectangle (A) is given by the equation L * W where L represents the length and<BR>\n" );
document.write( "W represents 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+%2A+W ALIGN=MIDDLE  ALT=\"A+=+L+%2A+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem tells you that the area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+5x ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you can put this into the equation<BR>\n" );
document.write( "in place of A to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+5x+=+L+%2A+W ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+5x+=+L+%2A+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the problem also tells you that the length of the rectangle is x.  So you can put x <BR>\n" );
document.write( "into the equation in place of L.  The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+5x+=+x+%2A+W ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+5x+=+x+%2A+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can now solve for W by dividing both sides of the equation by the multiplier of W which<BR>\n" );
document.write( "is x.  Dividing both sides by x results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+%2B+5x%29%2Fx+=+%28x%2AW%29%2Fx ALIGN=MIDDLE  ALT=\"%283x%5E2+%2B+5x%29%2Fx+=+%28x%2AW%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side, the x in the denominator must be divided into each of the two terms in<BR>\n" );
document.write( "the numerator.  When you divide the x into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can do so by recognizing<BR>\n" );
document.write( "that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+x%2Ax ALIGN=MIDDLE  ALT=\"x%5E2+=+x%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So you are really dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2Ax%2Fx ALIGN=MIDDLE  ALT=\"3%2Ax%2Ax%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the effect is that<BR>\n" );
document.write( "the x in the denominator cancels with one of the x terms in the numerator. So the problem<BR>\n" );
document.write( "can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%2Ax+%2B+5%2Ax%29%2Fx+=+%28x%2AW%29%2Fx ALIGN=MIDDLE  ALT=\"%283%2Ax%2Ax+%2B+5%2Ax%29%2Fx+=+%28x%2AW%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and canceling like x terms in the numerators and denominator results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%2Across%28x%29+%2B+5%2Across%28x%29%29%2Fcross%28x%29+=+%28cross%28x%29%2AW%29%2Fcross%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the answer becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax+%2B+5+=+W ALIGN=MIDDLE  ALT=\"3%2Ax+%2B+5+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that's the answer ... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+3x+%2B+5 ALIGN=MIDDLE  ALT=\"W+=+3x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and the steps you can take to solve it. </SPAN>\n" );
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