document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256781>Question 256781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the length and width of a rectangle were each increased by 1, the area would be<BR>\n" );
document.write( "84. The area would be 48 if the length and width were each diminished by 1.<BR>\n" );
document.write( "Find the perimeter of the original rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188826 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=188826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let L = length and W = width.\r<BR>\n" );
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document.write( "area = L*W\r<BR>\n" );
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document.write( "(L+1)*(W+1) = 84\r<BR>\n" );
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document.write( "(L-1)*(W-1) = 48\r<BR>\n" );
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document.write( "multiply these out to get:\r<BR>\n" );
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document.write( "LW + L + W + 1 = 84<BR>\n" );
document.write( "LW - L - W + 1 = 48\r<BR>\n" );
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document.write( "add both these equations together to get:\r<BR>\n" );
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document.write( "2LW + 2 = 132\r<BR>\n" );
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document.write( "subtract 2 from both sides of these equations to get:\r<BR>\n" );
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document.write( "2LW = 130\r<BR>\n" );
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document.write( "divide both sides of these equations by 2 to get:\r<BR>\n" );
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document.write( "LW = 65\r<BR>\n" );
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document.write( "substitute for LW in the original 2 equations to get:\r<BR>\n" );
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document.write( "LW + L + W + 1 = 84<BR>\n" );
document.write( "LW - L - W + 1 = 48\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "65 + L + W + 1 = 84<BR>\n" );
document.write( "65 - L - W + 1 = 48\r<BR>\n" );
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document.write( "subtract 66 from both sides of these equations to get:\r<BR>\n" );
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document.write( "L + W = 18<BR>\n" );
document.write( "-L -W = -18\r<BR>\n" );
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document.write( "Solve for L in each equation to get:\r<BR>\n" );
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document.write( "L = 18 - W (same answer for each equation).\r<BR>\n" );
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document.write( "You have a value for L in relation to W.\r<BR>\n" );
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document.write( "substitute for L in the first original equation to get:\r<BR>\n" );
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document.write( "(L+1)*(W+1) = 84 becomes:\r<BR>\n" );
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document.write( "(18-W+1) * (W+1) = 84\r<BR>\n" );
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document.write( "simplify each factor to get:\r<BR>\n" );
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document.write( "(19-W) * (W + 1) = 84\r<BR>\n" );
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document.write( "multiply out the factors to get:\r<BR>\n" );
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document.write( "19W + 19 - W^2 - W = 84\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "-W^2 + 18W + 19 = 84\r<BR>\n" );
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document.write( "subtract 84 from both sides of the equation to get:\r<BR>\n" );
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document.write( "-W^2 + 18W - 65 = 0\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get:\r<BR>\n" );
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document.write( "W^2 - 18W + 65 = 0\r<BR>\n" );
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document.write( "factor to get:\r<BR>\n" );
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document.write( "(W-13) * (W - 5) = 0\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "W = 13 or W = 5\r<BR>\n" );
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document.write( "since L = 18 - W, then you also get:\r<BR>\n" );
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document.write( "When W = 13, L = 5<BR>\n" );
document.write( "When W = 5, L = 13\r<BR>\n" );
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document.write( "substitute these values in the original equations to get:\r<BR>\n" );
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document.write( "When W = 13 and L = 5, then:\r<BR>\n" );
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document.write( "(L+1)*(W+1) = 84<BR>\n" );
document.write( "(L-1)*(W-1) = 48\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "6*14 = 84<BR>\n" );
document.write( "4*12 = 48\r<BR>\n" );
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document.write( "When W = 5 and L = 13, then:\r<BR>\n" );
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document.write( "(L+1)*(W+1) = 84<BR>\n" );
document.write( "(L-1)*(W-1) = 48\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "14*6 = 84<BR>\n" );
document.write( "12*4 = 48\r<BR>\n" );
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document.write( "all equations are true so the values for L and W are good.\r<BR>\n" );
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document.write( "Perimeter = 2L + 2W.\r<BR>\n" );
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document.write( "When L = 5 and W = 13, perimeter becomes 10 + 26 = 36\r<BR>\n" );
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document.write( "When L = 13 and W = 5, perimeter becomes 26 + 10 = 36\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "perimeter = 36\r<BR>\n" );
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document.write( " </SPAN>\n" );
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