document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98653>Question 98653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions of a rectangle whose area is 180cm^2 and whose perimeter is 54 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71794 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:\r<BR>\n" );
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document.write( "Find the dimensions of a rectangle whose area is 180cm^2 and whose perimeter is 54 cm.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Given that, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+180+cm%5E2+ ALIGN=MIDDLE  ALT=\"Area+=+180+cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+perimeter+=+54+cm+ ALIGN=MIDDLE  ALT=\"+perimeter+=+54+cm+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Perimeter of rectangle is given by the formula, 2( length + width)\r<BR>\n" );
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document.write( "==> 2( length + width) = 54\r<BR>\n" );
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document.write( "==>  ( length + width) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+54%2F2 ALIGN=MIDDLE  ALT=\"+54%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> ( length + width) = 27\r<BR>\n" );
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document.write( "Now suppose, length = x cm\r<BR>\n" );
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document.write( "Then width = 27 - x \r<BR>\n" );
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document.write( "Now area is given by the formula, length * width\r<BR>\n" );
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document.write( "That is length * width = 180 cm^2\r<BR>\n" );
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document.write( "==> x * ( 27-x) = 180\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27x+-+x%5E2+=+180+ ALIGN=MIDDLE  ALT=\"+27x+-+x%5E2+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+27+x+%2B+180+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+27+x+%2B+180+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----------------(1) \r<BR>\n" );
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document.write( "This is a quadratic equation and you can solve this equation using quadratic formula for x.\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "Comparing equation(1) with the standard quadratic equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have,\r<BR>\n" );
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document.write( "a = 1, b = -27 and c = 180\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-27%29+%2B-+sqrt%28%28-27%29%5E2-4%2A1%2A180+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29+%2B-+sqrt%28%28-27%29%5E2-4%2A1%2A180+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+27+%2B-+sqrt%28729-720%29%29+%2F+2++ ALIGN=MIDDLE  ALT=\"x+=+%28+27+%2B-+sqrt%28729-720%29%29+%2F+2++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+27+%2B-+sqrt+9+%29+%2F2++ ALIGN=MIDDLE  ALT=\"x+=+%28+27+%2B-+sqrt+9+%29+%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28+27+%2B+-+3%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28+27+%2B+-+3%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> either, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%2827+%2B+3%29%2F2 ALIGN=MIDDLE  ALT=\"+x+=+%2827+%2B+3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%2827+-+3%29%2F2 ALIGN=MIDDLE  ALT=\"+x+=+%2827+-+3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> either, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+30+%2F2 ALIGN=MIDDLE  ALT=\"+x+=+30+%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+24%2F2 ALIGN=MIDDLE  ALT=\"+x+=+24%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> either, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+15 ALIGN=MIDDLE  ALT=\"+x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+12 ALIGN=MIDDLE  ALT=\"+x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that is either length = 15 cm of 12 cm\r<BR>\n" );
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document.write( "When length = 15 cm, width =  27 - 15 = 12 cm\r<BR>\n" );
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document.write( "And when length = 12cm, width = 27 - 12 = 15 cm.\r<BR>\n" );
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document.write( "Hence the solution.\r<BR>\n" );
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document.write( "Hope you found the explanation useful.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseena.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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