document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=660443>Question 660443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the area of a square is numerically 117 more than the perimeter. Find the length of the side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411222 by </B><A HREF=/tutors/aboutme.mpl?userid=kevwill><B>kevwill(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kevwill><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=kevwill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=411222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s be the length of a side of the square.  Then the perimeter of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2As ALIGN=MIDDLE  ALT=\"4%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+=+4s+%2B+117 ALIGN=MIDDLE  ALT=\"s%5E2+=+4s+%2B+117\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+-+4s+-+117+=+0 ALIGN=MIDDLE  ALT=\"s%5E2+-+4s+-+117+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring this equation gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s+-+13%29%28s+%2B+9%29+=+0 ALIGN=MIDDLE  ALT=\"%28s+-+13%29%28s+%2B+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we have s = 13 or s = -9.  Since the side of a square cannot have negative length, the side must be 13.  The perimeter would be 52 and the area would be 169.<BR>\n" );
document.write( "You could also use the quadratic equation <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;\" > to solve for s, with a=1, b=-4 and c=-117. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );