document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106691>Question 106691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular corral built with 190 m of fencing that inludes four separate grazing areas lies on a 962 m(square) rectangular plot of land. the fence that divides the grazing areas is parallel to two of the sides of the corral. if there is a 1 m strip of land between each side of the corral and the property line, find the dimesions of the corral. there may be more than one answer!!... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77647 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L*w=A<BR>\n" );
document.write( "2L+2w=P<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L*w=926<BR>\n" );
document.write( "Our 2nd formula  uses the perimeter formula plus the extra fencing to divide the corral in quarters. We have to use 3 instead of 2 for the coeficients of L and w because of the extra fencing to divide the coral into 4ths. we also have to subtract 2 from L and w to account for the 1 m strip of land not used for the corral<BR>\n" );
document.write( "3(L-2)+3(w-2)=190<BR>\n" );
document.write( "3L-6+3w-6=190<BR>\n" );
document.write( "3L+3w-12=190<BR>\n" );
document.write( "3L+3w=190+12<BR>\n" );
document.write( "3L+3w=202<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A) L*w=926<BR>\n" );
document.write( "B) 3L+3w=202<BR>\n" );
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document.write( "L=926/w<BR>\n" );
document.write( "3(926/w)+3w=202 substitute 926/w for L<BR>\n" );
document.write( "2778/w+3w=202<BR>\n" );
document.write( "2778+3w^2=202w multiply each side by w to eliminate the fraction.<BR>\n" );
document.write( "3w^2-202w+2778=0<BR>\n" );
document.write( "Quadratic Formula (see below): w=19.26 m, w= 48.06<BR>\n" );
document.write( "I made L= 48.06 m and w= 19.26 m<BR>\n" );
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document.write( "Ed<BR>\n" );
document.write( " <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-202x%2B2778+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-202x%2B2778+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-202%29%5E2-4%2A3%2A2778=7468 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-202%29%5E2-4%2A3%2A2778=7468\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=7468 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--202%2B-sqrt%28+7468+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--202%2B-sqrt%28+7468+%29%29%2F2%5Ca\"   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=x%5B1%5D+=+%28-%28-202%29%2Bsqrt%28+7468+%29%29%2F2%5C3+=+48.0695984669789 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-202%29%2Bsqrt%28+7468+%29%29%2F2%5C3+=+48.0695984669789\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-202%29-sqrt%28+7468+%29%29%2F2%5C3+=+19.2637348663545 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-202%29-sqrt%28+7468+%29%29%2F2%5C3+=+19.2637348663545\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-202x%2B2778 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-202x%2B2778\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-202x%2B2778+=+%28x-48.0695984669789%29%2A%28x-19.2637348663545%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-202x%2B2778+=+%28x-48.0695984669789%29%2A%28x-19.2637348663545%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 48.0695984669789, 19.2637348663545.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-202%2Ax%2B2778+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-202%2Ax%2B2778+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C75%2C-750%2C100%2C3x%5E2-202x%2B2778%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C75%2C-750%2C100%2C3x%5E2-202x%2B2778%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );