document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25382>Question 25382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem is under Chapter 5, pg. 194 #32 in a Houghton Mifflin Math book.  It is really hard,and I am desperate for help.\r<BR>\n" );
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document.write( "There is a figure drawn with Trapezoid ABCD with Median MN.  Then there are diagonals AC and DB with the Intersecting points, E and F, respectively.  The problem is: If DC=3x, AB=2xsquared, and EF=7, find the value of X.\r<BR>\n" );
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document.write( "Please Help!!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13626 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is a figure drawn with Trapezoid ABCD with Median MN.  Then there are diagonals AC and DB with the Intersecting points, E and F, respectively.  The problem is: If DC=3x, AB=2xsquared, and EF=7, find the value of X.<BR>\n" );
document.write( "THOUGH , I DONOT HAVE YOUR BOOK ,YOU SHOULD BE HAVING IT.SO FOLLOW THE DIAGRAM FROM THE BOOK.I SHALL FOLLOW THE SAME NOMENCLATURE GIVEN BY YOU.O.K?<BR>\n" );
document.write( "ABCD IS THE TRAPEZIUM.LET AB BE THE BOTTOM SIDE AND DC THE TOP SIDE.M IS THE MID POINT OF AD,AND N IS THE MID POINT OF BC.MN IS  THE MEDIAN.JOIN AC AND BD THE DIAGONALS.LET AC CUT MN AT E AND BD CUT MN AT F.WE ARE GIVEN <BR>\n" );
document.write( "EF=7<BR>\n" );
document.write( "AB=2X^2<BR>\n" );
document.write( "DC=3X<BR>\n" );
document.write( "NOW MEDIAN IN A TRAPEZIUM IS PARALLEL TO THE 2 PARALLEL SIDES AB AND DC AND IS HALF THE SUM OF THE 2 PARALLEL SIDES .THAT IS <BR>\n" );
document.write( "MN = (AB+DC)/2=(2X^2+3X)/2<BR>\n" );
document.write( "AGAIN ,WE HAVE 3 PARALLEL LINES AB,DC AND MN.ONE TRANSVERSAL AD CUTS THEM IN EQUAL PARTS.(AM=MD).HENCE ANY OTHER TRANSVERSAL ALSO CUTS THEM IN EQUAL PARTS.<BR>\n" );
document.write( "HENCE FOR TRANSVERSAL DFB WE HAVE <BR>\n" );
document.write( "DF=FB <BR>\n" );
document.write( "AND FOR TRANSVERSAL CEA WE HAVE <BR>\n" );
document.write( "CE=EA.<BR>\n" );
document.write( "NOW IN TRIANGLE DAB , MF IS THE LINE JOINING MIDPOINTS OF DA AND DB.HENCE <BR>\n" );
document.write( "MF=AB/2=2X^2/2=X^2....<BR>\n" );
document.write( "SIMILARLY IN TRIANGLE CAB , EN IS THE LINE JOINING MIDPOINTS OF CA AND AB.HENCE <BR>\n" );
document.write( "EN=AB/2=2X^2/2=X^2.......NOW<BR>\n" );
document.write( "MN=(2X^2+3X)/2=MF+FN=MF+EN-EF= X^2+X^2-7 =2X^2-7....OR<BR>\n" );
document.write( "2X^2+3X=2(2X^2-7)=4X^2-14<BR>\n" );
document.write( "4X^2-14-2X^2-3X=0<BR>\n" );
document.write( "2X^2-3X-14=0<BR>\n" );
document.write( "2X^2-7X+4X-14=0<BR>\n" );
document.write( "X(2X-7)+2(2X-7)=0<BR>\n" );
document.write( "(2X-7)(X+2)=0<BR>\n" );
document.write( "2X-7=0<BR>\n" );
document.write( "X=7/2=3.5\r<BR>\n" );
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