document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107935>Question 107935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a rectangle is 2 ft longer than its length and 5 feet longer than its width. What are the dimensions of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78686 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=78686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal divides the rectangle into 2 equal right triangles.<BR>\n" );
document.write( "Let the diagonal=c and the 2 sides be a and b.<BR>\n" );
document.write( "a=c-2, b=c-5<BR>\n" );
document.write( "a^2+b^2=c^2<BR>\n" );
document.write( "(c-2)^2+(c-5)^2=c^2<BR>\n" );
document.write( "c^2-4c+4+c^2-10c+25=c^2<BR>\n" );
document.write( "c^2-14c+29=0<BR>\n" );
document.write( "c^2-14c   =-29<BR>\n" );
document.write( "c^2-14c+49=49-29 complete the square<BR>\n" );
document.write( "(c-7)^2=20<BR>\n" );
document.write( "c-7=+-sqrt(20)<BR>\n" );
document.write( "c=7+-sqrt(5*4)<BR>\n" );
document.write( "=7+-2sqrt(5)<BR>\n" );
document.write( "Only 7+2sqrt(5) is the only correct answer for the diagonal. the other would lead to negative numbers for the sides of the rectangle.<BR>\n" );
document.write( "The sides of the rectangle are:<BR>\n" );
document.write( "5+2sqrt(5) and 2+2sqrt(5)<BR>\n" );
document.write( "Ed </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );