document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333343>Question 333343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two rectangles have the same area of 480 cm^2.the diffrence between their lengths is 5cm and the diffrence between their widths is 2cm . calculate the dimension of the rectangles </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238910 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two rectangles have the same area of 480 cm^2.<BR>\n" );
document.write( "the difference between their lengths is 5cm and the difference between their widths is 2cm.<BR>\n" );
document.write( " calculate the dimension of the rectangles<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the dimension of the original rectangle be L, W<BR>\n" );
document.write( "L*W = 480<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480%2FW ALIGN=MIDDLE  ALT=\"480%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "the dimensions of the other rectangle be (L-5), (w+2)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Areas of the two rectangles are equal<BR>\n" );
document.write( "(L-5)*(W+2) = L*W<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "LW + 2L - 5W - 10 = LW<BR>\n" );
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document.write( "Subtract LW from both sides<BR>\n" );
document.write( "2L - 5W - 10 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Replace L with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480%2FW ALIGN=MIDDLE  ALT=\"480%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480%2FW ALIGN=MIDDLE  ALT=\"480%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - 5W - 10 = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=960%2FW ALIGN=MIDDLE  ALT=\"960%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 5W - 10 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by W<BR>\n" );
document.write( "960 - 5W^2 - 10W = 0<BR>\n" );
document.write( ";<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "-5W^2 - 10w + 960 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "simplify, divide by -5<BR>\n" );
document.write( "W^2 + 2W - 192 = 0<BR>\n" );
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document.write( "Find W using the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "in this equation: x=w; a=1; b=2; c=-192<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-2+%2B-+sqrt%282%5E2-4%2A1%2A-192+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B-+sqrt%282%5E2-4%2A1%2A-192+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-2+%2B-+sqrt%284+-+%28-768%29+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B-+sqrt%284+-+%28-768%29+%29%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=w+=+%28-2+%2B-+sqrt%284+%2B+768+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B-+sqrt%284+%2B+768+%29%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=w+=+%28-2+%2B-+sqrt%28772+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B-+sqrt%28772+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "two solutions, but we just want the positive solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-2+%2B+27.785%29%2F2+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B+27.785%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25.785%2F2 ALIGN=MIDDLE  ALT=\"25.785%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = 12.89 cm, the width of the original rectangle <BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480%2F12.89 ALIGN=MIDDLE  ALT=\"480%2F12.89\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 37.24 cm is the original length<BR>\n" );
document.write( "Check area: 12.89*37.24 = 480.02 <BR>\n" );
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document.write( "The other rectangle<BR>\n" );
document.write( "12.89 + 2 = 14.89 is the width<BR>\n" );
document.write( "37.24 - 5 = 32.24 is the length<BR>\n" );
document.write( "check area: 14.89*32.24 = 480.05, close enough to confirm our solutions </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );