document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=13187>Question 13187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the first side of a triangle is 7cm shorter thatn twice the second side. the third side is 4cm longer than the first side. the perimeter is 80. find the length of each side. please help  me out with these problems. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6612 by </B><A HREF=/tutors/aboutme.mpl?userid=akmb1215><B>akmb1215(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=akmb1215><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=6612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing to do is to assign variables for the sides of the triangle.  I am going to call them X, Y, and Z.  The first side, X, is 7cm shorter than twice the second side, Y.  Written as an equation, this is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+Y+-+7 ALIGN=MIDDLE  ALT=\"X+=+Y+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then, you know that the third side, Z, is 4cm longer than the first side.  WRite as an equation, this is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+X+%2B+4 ALIGN=MIDDLE  ALT=\"Z+=+X+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The perimeter, which is the sides added together, is 80.  So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+Y+%2B+Z+=+80 ALIGN=MIDDLE  ALT=\"X+%2B+Y+%2B+Z+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
document.write( "\n" );
document.write( "To solve this, you will need to figure out a way to get X + Y + Z = 80 to have only 1 variable in it. Since you know that Z = X + 4, you can plug X + 4 in for Z in that equation.  Now you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+Y+%2B+X+%2B+4+=+80 ALIGN=MIDDLE  ALT=\"X+%2B+Y+%2B+X+%2B+4+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  For the first equation we wrote, solve for Y, which makes the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+X+%2B+7 ALIGN=MIDDLE  ALT=\"Y+=+X+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now plug this in for Y in the longer equation, which changes it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+X+%2B+7+%2B+X+%2B+4+=+80 ALIGN=MIDDLE  ALT=\"X+%2B+X+%2B+7+%2B+X+%2B+4+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  To solve the equation, add like terms, which changes the equation to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X+%2B+11+=+80 ALIGN=MIDDLE  ALT=\"3X+%2B+11+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Move the 11 to the right side of the equation, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X+=+69 ALIGN=MIDDLE  ALT=\"3X+=+69\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Solve for X (X = 23).  To figure out Y and Z, simply plug 23 in for X in the original equations.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23+=+Y+-+7 ALIGN=MIDDLE  ALT=\"23+=+Y+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >; Y=30.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+23+%2B+4 ALIGN=MIDDLE  ALT=\"Z+=+23+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; Z=27. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );