document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595488>Question 595488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 38 inches, and its area is 88 in2. Find the length of the longer and shorter side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377176 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=377176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "We can solve this problem using a system of equations.<BR>\n" );
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document.write( "[I]Define your variables.<BR>\n" );
document.write( "L = the longer side<BR>\n" );
document.write( "S = the shorter side\r<BR>\n" );
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document.write( "[II] Write the system of equations.<BR>\n" );
document.write( "We will need to use the formulas for the perimeter of a rectangle and for the area of a rectangle to write our equations. <BR>\n" );
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document.write( "The PERIMETER is the distance around the edge of the rectangle, so an algebraic expression for the perimeter is S+L+S+L. We can simplify this to 2S+2L. Since the perimeter is 38 inches, our first equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%2B2L=38 ALIGN=MIDDLE  ALT=\"2S%2B2L=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The AREA is the space inside the rectangle, so an algebraic expression for the area is (S)(L). Since the area is 88 square inches, our second equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%29%28L%29=88 ALIGN=MIDDLE  ALT=\"%28S%29%28L%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "[III] Solve the system of equations.<BR>\n" );
document.write( "Let's use the substitution method. Rewrite the first equation to isolate S.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%2B2L=38 ALIGN=MIDDLE  ALT=\"2S%2B2L=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S=38-2L ALIGN=MIDDLE  ALT=\"2S=38-2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%2838-2L%29%2F2 ALIGN=MIDDLE  ALT=\"S=%2838-2L%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=19-L ALIGN=MIDDLE  ALT=\"S=19-L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 19-L for S in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%29%28L%29=88 ALIGN=MIDDLE  ALT=\"%28S%29%28L%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819-L%29%28L%29=88 ALIGN=MIDDLE  ALT=\"%2819-L%29%28L%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify (you'll get a quadratic equation) and solve for L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19L-L%5E2=88 ALIGN=MIDDLE  ALT=\"19L-L%5E2=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rearrange the equation and set it equal to 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-L%5E2%2B19L-88=0 ALIGN=MIDDLE  ALT=\"-L%5E2%2B19L-88=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply every term by -1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2-19L%2B88=0 ALIGN=MIDDLE  ALT=\"L%5E2-19L%2B88=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation factors nicely since (-11)(-8)=88 and (-11)+(-8)=-19.<BR>\n" );
document.write( ". <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-11%29%28L-8%29=0%29 ALIGN=MIDDLE  ALT=\"%28L-11%29%28L-8%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We use the zero-product property to say that either<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L-11=0 ALIGN=MIDDLE  ALT=\"L-11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L-8=0 ALIGN=MIDDLE  ALT=\"L-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=11 ALIGN=MIDDLE  ALT=\"L=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=8 ALIGN=MIDDLE  ALT=\"L=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Either the longer side is 11 inches or 8 inches. Clearly the longer side L is 11 inches since 11 is greater than 8. The shorter side S is 8 inches.<BR>\n" );
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document.write( "[IV] Check your work checking the perimeter and area for these values!<BR>\n" );
document.write( "Perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B2S=38 ALIGN=MIDDLE  ALT=\"2L%2B2S=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2811%29%2B2%288%29=38 ALIGN=MIDDLE  ALT=\"2%2811%29%2B2%288%29=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2B16=38 ALIGN=MIDDLE  ALT=\"22%2B16=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38=38 ALIGN=MIDDLE  ALT=\"38=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Perfect!<BR>\n" );
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document.write( "Area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%29%28L%29=88 ALIGN=MIDDLE  ALT=\"%28S%29%28L%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%2811%29=88 ALIGN=MIDDLE  ALT=\"%288%29%2811%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=88=88 ALIGN=MIDDLE  ALT=\"88=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Winner, winner, chicken dinner!<BR>\n" );
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document.write( "That's it. Feel free to email me if you have questions about the solution.<BR>\n" );
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document.write( "Good luck,<BR>\n" );
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document.write( "Mrs.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );