document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464769>Question 464769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 34cm, and the diagonal is 13cm. Determine the lengths of the sides of the rectangle. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I need to set this up in a quadratic equation then solve. I have several problems like this and knowing how to set them up would be a big help. Thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318420 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=318420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 34cm, and the diagonal is 13cm. Determine the lengths of the sides of the rectangle.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "let x=length of rectangle<BR>\n" );
document.write( "let y=width of rectangle<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2x+2y=perimeter=34<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "x+y=17<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2+y^2=13^2=169  (Pythagorean Theorem)<BR>\n" );
document.write( "y^2=169-x^2<BR>\n" );
document.write( "y=ħsqrt(169-x^2)<BR>\n" );
document.write( "since y>0, use the positive sqrt<BR>\n" );
document.write( "x+y=17<BR>\n" );
document.write( "x+sqrt(169-x^2)=17<BR>\n" );
document.write( "sqrt(169-x^2)=17-x<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "169-x^2=289-34x+x^2<BR>\n" );
document.write( "2x^2-34x+120=0<BR>\n" );
document.write( "x^2-17x+60=0<BR>\n" );
document.write( "(x-5)(x-12)=0<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "y=17-x=12<BR>\n" );
document.write( "or <BR>\n" );
document.write( "x=12<BR>\n" );
document.write( "y=17-x=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "length of rectangle=5<BR>\n" );
document.write( "Width of rectangle=12 <BR>\n" );
document.write( "or<BR>\n" );
document.write( "length of rectangle=12<BR>\n" );
document.write( "Width of rectangle=5  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );