document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461444>Question 461444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 100 m.  The length is 18 m more than twice the width.  Find the dimensions, length and width. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316454 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=316454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, think of the definition of perimeter as it applies to a rectangle.  The perimeter is equal to the sum of the sides. In a rectangle there are two lengths and two widths. Let L represent the length and W represent the width.  Therefore, you can write that the perimeter (P) is equal to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+L+%2B+W+%2B+L+%2B+W+=+2L+%2B+2W ALIGN=MIDDLE  ALT=\"P+=+L+%2B+W+%2B+L+%2B+W+=+2L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But you are told that the length is equal to 18 m more than twice 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=L+=+18+%2B+2W ALIGN=MIDDLE  ALT=\"L+=+18+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So return to the perimeter equation and substitute 18 + 2W for L and the perimeter equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+2%2818%2B2W%29+%2B+2W ALIGN=MIDDLE  ALT=\"P+=+2%2818%2B2W%29+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Perform distributive multiplication on the term inside the parentheses by multiplying 2 times each of the quantities inside the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+36+%2B+4W+%2B+2W ALIGN=MIDDLE  ALT=\"P+=+36+%2B+4W+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the two terms 4W and 2W by adding them to get 6W and the perimeter equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+36+%2B+6W ALIGN=MIDDLE  ALT=\"P+=+36+%2B+6W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now recognize that the problem tells you that the perimeter equals 100 m. So you can substitute 100 for P to get the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+=+36+%2B+6W ALIGN=MIDDLE  ALT=\"100+=+36+%2B+6W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 36 on the right side of the equation by subtracting 36 from both sides and the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+6W ALIGN=MIDDLE  ALT=\"64+=+6W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can solve for the width W by dividing both sides of this equation by 6 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.666666666+=+W ALIGN=MIDDLE  ALT=\"10.666666666+=+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recognize that 0.66666666 ... is the decimal form of the fraction 2/3.<BR>\n" );
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document.write( "and don't forget the units ... W, the width, is 10 and 2/3 meters.<BR>\n" );
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document.write( "Now return to the equation that told you that the length, L, was 18 m longer than 2W.  Since W is 10.6666666 ... meters, then twice W is 21.3333333 ... m and 18 m more than that is 18 + 21.33333333 ... = 39 and 1/3 m. So the length is 39 and 1/3 m. (Recognize again that 0.333333 ... is the decimal equivalent of the fraction 1/3.)<BR>\n" );
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document.write( "Check to see that in a rectangle that is 39 and 1/3 meters long and 10 and 2/3 meter wide, the perimeter is 100 meters by adding up the four sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%2839%2B1%2F3%29+%2B+%2810%2B2%2F3%29+%2B+%2839%2B1%2F3%29+%2B+%2810%2B2%2F3%29 ALIGN=MIDDLE  ALT=\"P+=+%2839%2B1%2F3%29+%2B+%2810%2B2%2F3%29+%2B+%2839%2B1%2F3%29+%2B+%2810%2B2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you do this addition, you will find that the sum is 100 meters so the solution you have is correct.<BR>\n" );
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document.write( "Hope this helps you understand the problem a little better. </SPAN>\n" );
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