document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622247>Question 622247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 6 cm longer than its width. If the perimeter of the rectangle is 48 cm, find its area.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391330 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Here is one way to solve this problem.<BR>\n" );
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document.write( "Let W be the width of the rectangle.<BR>\n" );
document.write( "Let L be the length of the rectangle.<BR>\n" );
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document.write( "We need to write two equations that use the information in the problem to model the situation. <BR>\n" );
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document.write( "The perimeter is 48 cm. Perimeter is the distance around the the rectangle: two widths and two lengths.<BR>\n" );
document.write( "[two widths of the rectangle] + [two lengths of the rectangle] = [the perimeter]<BR>\n" );
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document.write( "In algebra, we write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B2L=48 ALIGN=MIDDLE  ALT=\"2W%2B2L=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We also know that the length of a rectangle is 6 cm longer than its width. <BR>\n" );
document.write( "[the length of the rectangle] = [the width of the rectangle] + [6 more centimeters]<BR>\n" );
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document.write( "In algebra, we write,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=W%2B6 ALIGN=MIDDLE  ALT=\"L=W%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we have a system of two equations. We will solve it using the substitution method. Substitute W+6 for L in the perimeter equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B2L=48 ALIGN=MIDDLE  ALT=\"2W%2B2L=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B2%28W%2B6%29=48 ALIGN=MIDDLE  ALT=\"2W%2B2%28W%2B6%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for W. Clear the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B2W%2B12=48 ALIGN=MIDDLE  ALT=\"2W%2B2W%2B12=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4W%2B12=48 ALIGN=MIDDLE  ALT=\"4W%2B12=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 12 form both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4W=48-12 ALIGN=MIDDLE  ALT=\"4W=48-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4W=36 ALIGN=MIDDLE  ALT=\"4W=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=9 ALIGN=MIDDLE  ALT=\"W=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The width of the rectangle is 9 cm. Since the length of the rectangle is 6 more the the width, the length is 15 cm.<BR>\n" );
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document.write( "The formula for the area of a rectangle is A=L*W. The area is 135 square cm since 9*15=135.<BR>\n" );
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document.write( "The last step to to check our answer against the original problem. The perimeter should be 48 cm. We see that 2 widths is 18 cm, and 2 lengths is 30 cm; 18+30=48. Check!<BR>\n" );
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document.write( "Please email me if I need to explain any part of this better. By the way, there is a way to solve this problem without using two variables and a system of equations. Let me know if you'd like to see that method.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
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