document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837711>Question 837711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of an airplane ticket is 30 centimeters. The area is 50 square centimeters. What are the dimensions of the ticket? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504727 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> perimeter is equal to 2L + 2W<BR>\n" );
document.write( "area is equal to L * W<BR>\n" );
document.write( "you get 2 equations:<BR>\n" );
document.write( "30 = 2L + 2W<BR>\n" );
document.write( "50 = L*W\r<BR>\n" );
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document.write( "we'll solve by substitution.<BR>\n" );
document.write( "you can use either equation to solve for either variable.\r<BR>\n" );
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document.write( "we'll use the second equation to solve for L.\r<BR>\n" );
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document.write( "second equation is:<BR>\n" );
document.write( "50 = L*W<BR>\n" );
document.write( "divide both sides of this equation by W to get:<BR>\n" );
document.write( "L = 50/W\r<BR>\n" );
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document.write( "we now have a value of L that we can substitute in the first equation which we can then use to solve for W.\r<BR>\n" );
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document.write( "the first equation is:<BR>\n" );
document.write( "30 = 2L + 2W<BR>\n" );
document.write( "replace L with 50/W to get:<BR>\n" );
document.write( "30 = 2*(50/W) + 2W<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "30 = 100/W + 2W<BR>\n" );
document.write( "multiply both sides of this equation by W to get:<BR>\n" );
document.write( "30W = 100 + 2W^2<BR>\n" );
document.write( "subtract 30W from both sides of this equation to get:<BR>\n" );
document.write( "2W^2 - 30W + 100 = 0<BR>\n" );
document.write( "factor this equation to get:<BR>\n" );
document.write( "(2W - 20) * (W - 5) = 0<BR>\n" );
document.write( "solve for W to get:<BR>\n" );
document.write( "W = 10 or W = 5\r<BR>\n" );
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document.write( "if W = 10, then use the equation of 50 = L*W to get L = 5<BR>\n" );
document.write( "if W = 5, then use the equation of 50 = L*W to get L = 10\r<BR>\n" );
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document.write( "you have 2 possible solutions.<BR>\n" );
document.write( "L = 5 and W = 10 or:<BR>\n" );
document.write( "L = 10 and W = 5<BR>\n" );
document.write( "both are plausible so we'll test them both out.\r<BR>\n" );
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document.write( "when L = 5 and W = 10:<BR>\n" );
document.write( "the first equation becomes 2*5 + 2*10 = 10 + 20 = 30 <BR>\n" );
document.write( "the second equation becomes 5*10 = 50<BR>\n" );
document.write( "both equations confirm that the solution of L = 5 and W = 10 is good.\r<BR>\n" );
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document.write( "when L = 10 andW = 5:<BR>\n" );
document.write( "the first equation becomes 2*10 + 2*5 = 20 + 10 = 30<BR>\n" );
document.write( "the second equation becomes 10*5 = 5<BR>\n" );
document.write( "both equations confirm that the solution of L = 10 and W = 5 is good.\r<BR>\n" );
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document.write( "the ticket can have either:\r<BR>\n" );
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document.write( "a length of 5 and a width of 10 or:<BR>\n" );
document.write( "a length of 10 and a width of 5.\r<BR>\n" );
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document.write( "since the length is usually longer than the width, you are free to choose that the ticket most likely  has a length of 10 and a width of 5.\r<BR>\n" );
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document.write( "alternatively, you can simply say that the dimensions are 5 by 10 and let the recipient of that information determine which is the length and which is the width.\r<BR>\n" );
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document.write( "mathematically, the length can be 10 and the width 5 or the length can be 5 and the width 10.  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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