document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164862>Question 164862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of one square exceeds that of another by 16 and its area is 44 less than 4 times the area of the other. What is the length of the side of each side of each square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121498 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=121498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let p1 = perimeter of one square.<BR>\n" );
document.write( "let p2 = perimeter of the other square.<BR>\n" );
document.write( "let a1 = area of one square.<BR>\n" );
document.write( "let a2 = area of the other square.<BR>\n" );
document.write( "let s1 = side of one square.<BR>\n" );
document.write( "let s2 = side of the other square.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "p1 = p2 + 16<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "perimeter of a square equals 4 times one side.<BR>\n" );
document.write( "p = 4*s<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "4s1 = 4s2 + 16 (first equation) *****<BR>\n" );
document.write( "s1 = (4s2 + 16)/4<BR>\n" );
document.write( "s1 = s2 + 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a1 = 4a2 - 14<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "area of a square equals one side times the other side (one side squared).<BR>\n" );
document.write( "a = s^2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "s1^2 = 4(s2^2) - 44 (second equation) *****<BR>\n" );
document.write( "since s1 = s2+4, this equation becomes<BR>\n" );
document.write( "(s2+4)^2 = 4(s2^2) - 44<BR>\n" );
document.write( "to make calculating less confusing, let x = s2<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "(x+4)^2 = 4x^2 - 44<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "x^2 + 8x + 16 = 4x^2 - 44<BR>\n" );
document.write( "subtract the equation on the left from both sides of the equation and it becomes<BR>\n" );
document.write( "0 = 4x^2 - 44 - x^2 - 8x - 16<BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "0 = 3x^2 - 8x - 60<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "3x^2 - 8x - 60 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that equation factors out to be<BR>\n" );
document.write( "(3x+10)*(x-6) = 0<BR>\n" );
document.write( "factors are:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = -10/3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the side of the square can't be negative, the only answer that looks promising is x = 6.<BR>\n" );
document.write( "since x = s2, that means that ...<BR>\n" );
document.write( "s2 = 6.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "first equation is reproduced here for ease of reference.<BR>\n" );
document.write( "4s1 = 4s2 + 16 (first equation) *****<BR>\n" );
document.write( "since s2 = 6, this equation becomes<BR>\n" );
document.write( "4s1 = 4*6 + 16 = 24 + 16 = 40<BR>\n" );
document.write( "s1 = 10.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "second equation is reproduced here for ease of reference.<BR>\n" );
document.write( "s1^2 = 4(s2^2) - 44 (second equation) *****<BR>\n" );
document.write( "since s1 = 10, and s2 = 6, this equation becomes<BR>\n" );
document.write( "10^2 = 4*(6^2) - 44<BR>\n" );
document.write( "100 = 4*36 - 44<BR>\n" );
document.write( "100 = 144 - 44<BR>\n" );
document.write( "100 = 100<BR>\n" );
document.write( "s1 and s2 yield correct values for the equations.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "s1 = 10 = side of one square.<BR>\n" );
document.write( "s2 = 6 = side of the other square.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );