document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134281>Question 1134281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a perimeter of 34cm. One of its diagonals is 13cm. Find its sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751629 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the perimeter of the rectangle is 34 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for perimeter is 2x + 2y = p\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when p = 34, the formula becomes 2x + 2y = 34\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the length<BR>\n" );
document.write( "y is the width\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "one of the diagonals is 13 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since it's a rectangle, the other diagonal has to be 13 as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's a nice fact to know but it's not necessary to know it to solve this problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the diagonal forms a right triangle with one of the sides being x and the other side being y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by pythagorus, the diagonal squared is equal to x^2 + y^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula is therefore x^2 + y^2 = 13^2 which becomes x^2 + y^2 = 169.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have two equations that needs to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are 2x + 2y = 34 and x^2 + y^2 = 169.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y in the first equation to get y = 17 - x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with 17 - x in the second equation to get x^2 + (17 - x)^2 = 169\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get x^2 + x^2 - 34x + 289 = 169\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 169 from both sides of that equation to get x^2 + x^2 - 34x + 120 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get 2x^2 - 34x + 120 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 2 to get x^2 - 17x + 60 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor that equation to get (x - 5) * (x - 12) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes x = 5 or x = 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since y = 17 - x, .....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 5, y = 12<BR>\n" );
document.write( "when x = 12, y = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x is the length of the rectangle, let x = 12.<BR>\n" );
document.write( "you have length of the rectangle is 12 and width of the rectangle is 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the perimeter is equal to 2 * 12 + 2 * 5 = 24 + 10 = 35 cm which is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 + y^2 = 13^2 becomes 12^2 + 5^2 = 169 which becomes 144 + 25 = 169 which becomes 169 = 169 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution looks good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution is that the length of the rectangle is 12 and the width of the rectangle is 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a good reference on the properties of a rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://brilliant.org/wiki/properties-of-rectangles/\" target = \"_blank\">https://brilliant.org/wiki/properties-of-rectangles/</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );