document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554970>Question 554970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the perimeter of a triangle is 52 cm the longest side is 2 cm less than the sum of the other 2 sides twice the shortest side is 15 centimeters less than the longest side find the lengths of each side of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361590 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=361590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the triangle be have sides of a, b, and c<BR>\n" );
document.write( "let p equal the perimeter.<BR>\n" );
document.write( "p = a + b + c<BR>\n" );
document.write( "p = 52 cm.<BR>\n" );
document.write( "let a be the longest side.<BR>\n" );
document.write( "since the longest side is equal to 2 less than the sum of the other 2 sides, you get:<BR>\n" );
document.write( "a = b + c - 2<BR>\n" );
document.write( "let c be the shortest side.<BR>\n" );
document.write( "since 2 times the shortest side is equal to 5 less than the longest side, you get:<BR>\n" );
document.write( "2c = a - 15<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "a + b + c = 52<BR>\n" );
document.write( "a = b + c - 2<BR>\n" );
document.write( "2c = a - 15<BR>\n" );
document.write( "you can solve for b in terms of a and you can solve for c in terms of a.<BR>\n" );
document.write( "then you'll have an equation for the perimeter that only has \"a\" in it which will allow you to solve for \"a\".<BR>\n" );
document.write( "once you have solve for \"a\", you can then use the other equations to solve for b and c.<BR>\n" );
document.write( "take a = b + c - 2<BR>\n" );
document.write( "subtract c from both sides of the equation and add 2 to both sides of the equation to get:<BR>\n" );
document.write( "a - c + 2 = b<BR>\n" );
document.write( "this is the same as:<BR>\n" );
document.write( "b = a - c + 2<BR>\n" );
document.write( "take 2c = a - 15<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( "c = a/2 - 15/2<BR>\n" );
document.write( "you now have 3 equations to work with.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "p = a + b + c<BR>\n" );
document.write( "b = a - c + 2<BR>\n" );
document.write( "c = a/2 - 15/2<BR>\n" );
document.write( "in the equation of:<BR>\n" );
document.write( "b = a - c + 2<BR>\n" );
document.write( "you can substitute for c to get:<BR>\n" );
document.write( "b = a - c + 2 becomes:<BR>\n" );
document.write( "b = a - (a/2 - 15/2) + 2<BR>\n" );
document.write( "remove parentheses to get:<BR>\n" );
document.write( "b = a - a/2 + 15/2 + 2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "b = a/2 + 19/2<BR>\n" );
document.write( "you now have:<BR>\n" );
document.write( "p = a + b + c<BR>\n" );
document.write( "b = a/2 + 19/2<BR>\n" );
document.write( "c = a/2 - 15/2<BR>\n" );
document.write( "you can now subsitute for b and c in the equation of p = a + b + c to get:<BR>\n" );
document.write( "p = a + a/2 + 19/2 + a/2 - 15/2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "p = 2a + 2<BR>\n" );
document.write( "since p = 52, you get:<BR>\n" );
document.write( "52 = 2a + 2<BR>\n" );
document.write( "subtract 2 from both sides of this equation to get:<BR>\n" );
document.write( "50 = 2a.<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( "a = 25.<BR>\n" );
document.write( "from the equation b = a/2 + 19/2, you will get:<BR>\n" );
document.write( "b = 25/2 + 19/2 which becomes:<BR>\n" );
document.write( "b = 44/2 which becomes:<BR>\n" );
document.write( "b = 22<BR>\n" );
document.write( "from the equation c = a/2 - 15/2, you will get:<BR>\n" );
document.write( "c = 25/2 - 15/2 which becomes:<BR>\n" );
document.write( "c = 10/2 which becomes:<BR>\n" );
document.write( "c = 5.<BR>\n" );
document.write( "you now have:<BR>\n" );
document.write( "a = 25<BR>\n" );
document.write( "b = 22<BR>\n" );
document.write( "c = 5<BR>\n" );
document.write( "p = a + b + c = 25 + 22 + 5 = 25 + 27 = 52.<BR>\n" );
document.write( "looks like it works out and that's your answer.<BR>\n" );
document.write( "the longest side is 25 and the middle size is 22 and the shortest side is 5.<BR>\n" );
document.write( "confirm by going back to the original problem statement.<BR>\n" );
document.write( "it says:<BR>\n" );
document.write( "the longest side is 2 cm less than the sum of the other 2 sides.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "25 = 22 + 5 - 2 which becomes:<BR>\n" );
document.write( "25 = 27 - 2 which becomes:<BR>\n" );
document.write( "25 = 25 ***** longest side length is confirmed.<BR>\n" );
document.write( "2 times the shortest side is 15 cm less than the longest side.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "2*5 = 25 - 15 which become:<BR>\n" );
document.write( "10 = 10 ***** shortest side is confirmed.<BR>\n" );
document.write( "everything check out ok so the answer is confirmed as correct.<BR>\n" );
document.write( "longest side is 25<BR>\n" );
document.write( "middle side is 22<BR>\n" );
document.write( "shortest side is 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );