document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197235>Question 1197235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is it possible to have a rectangular property which has perimeter of 78 m and an area of 395m^2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830427 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "L = length<BR>\n" );
document.write( "W = width\r<BR>\n" );
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document.write( "P = perimeter of a rectangle<BR>\n" );
document.write( "P = 2(L+W) = 2L+2W\r<BR>\n" );
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document.write( "Replace P with the stated perimeter 78 and let's isolate L<BR>\n" );
document.write( "P = 2L+2W<BR>\n" );
document.write( "78 = 2L+2W<BR>\n" );
document.write( "78/2 = 2L/2+2W/2<BR>\n" );
document.write( "39 = L+W<BR>\n" );
document.write( "L = 39-W\r<BR>\n" );
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document.write( "A = area of a rectangle<BR>\n" );
document.write( "A = LW<BR>\n" );
document.write( "A = (39-W)W<BR>\n" );
document.write( "A = -W^2+39W\r<BR>\n" );
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document.write( "Plug in the stated area A = 395<BR>\n" );
document.write( "I'll replace each W with x<BR>\n" );
document.write( "A = -W^2+39W<BR>\n" );
document.write( "395 = -x^2+39x<BR>\n" );
document.write( "395+x^2-39x = 0<BR>\n" );
document.write( "x^2-39x+395 = 0\r<BR>\n" );
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document.write( "Use the quadratic formula to solve for x. <BR>\n" );
document.write( "Use a = 1, b = -39, c = 395.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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-%28-39%29%2B-sqrt%28%28-39%29%5E2-4%281%29%28395%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-39%29%2B-sqrt%28%28-39%29%5E2-4%281%29%28395%29%29%29%2F%282%281%29%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+=+%2839%2B-sqrt%281521-1580%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2839%2B-sqrt%281521-1580%29%29%2F%282%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+=+%2839%2B-sqrt%28-59%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2839%2B-sqrt%28-59%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+b%5E2+-+4ac+=+%28-39%29%5E2-4%281%29%28395%29+=+-59 ALIGN=MIDDLE  ALT=\"d+=+b%5E2+-+4ac+=+%28-39%29%5E2-4%281%29%28395%29+=+-59\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, so there are no real number solutions.<BR>\n" );
document.write( "The two roots of x^2-39x+395 = 0 are complex numbers in the form a+bi where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If your teacher hasn't covered complex or imaginary numbers just yet, then ignore this subsection. <BR>\n" );
document.write( "The summary is that x^2-39x+395 = 0  has no real solutions.\r<BR>\n" );
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document.write( "Since x^2-39x+395 = 0 has no real solutions, this means we <u>cannot</u> have a rectangle with perimeter 78 meters and area 395 square meters.<BR>\n" );
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