document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027714>Question 1027714</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular countertop has an area of 27 square feet. Its perimeter is 24 feet. What are the dimensions of the counter?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643017 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "A rectangular countertop <BR>\n" );
document.write( "has an area of 27 square feet.<BR>\n" );
document.write( "Area = length x breadth<BR>\n" );
document.write( "xy = 27.......(1)<BR>\n" );
document.write( "x = 27/y.......(1)<BR>\n" );
document.write( "Its perimeter is 24 feet.<BR>\n" );
document.write( "Perimeter = 2 x width + 2 x length<BR>\n" );
document.write( "24 = 2x + 2y<BR>\n" );
document.write( "2x + 2y = 24.......(2)<BR>\n" );
document.write( "Substitute x = 27/y into Eq(2)<BR>\n" );
document.write( "2(27/y) + 2y = 24<BR>\n" );
document.write( "54/y + 2y = 24<BR>\n" );
document.write( "Multiply through by y<BR>\n" );
document.write( "54 + 2y^2 = 24y<BR>\n" );
document.write( "Sort into ax^2 + bx + c form<BR>\n" );
document.write( "2y^2 - 24y + 54<BR>\n" );
document.write( "Divide by 2<BR>\n" );
document.write( "2(y^2 - 12y + 27)= 0<BR>\n" );
document.write( "2(y - 3)(y - 9) = 0<BR>\n" );
document.write( "y - 3 = 0 <BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "y - 9 = 0<BR>\n" );
document.write( "y = 9<BR>\n" );
document.write( "By substituting either y = 3<BR>\n" );
document.write( "back into Eq(1)<BR>\n" );
document.write( "x = 27/y<BR>\n" );
document.write( "x = 27/3<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "or Substituting y = 9<BR>\n" );
document.write( "back into Eq(1)<BR>\n" );
document.write( "x = 27/y<BR>\n" );
document.write( "x = 27/9<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "So, either your breadth is 3ft<BR>\n" );
document.write( "and the length is 9ft<BR>\n" );
document.write( "or<BR>\n" );
document.write( "breadth is 9ft<BR>\n" );
document.write( "and the length is 3ft<BR>\n" );
document.write( "Hope this helps :-) </SPAN>\n" );
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