document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28582>Question 28582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectancle JKLM is inscribed in an another rectangle ABCD such that the vertices J,K,L and M touches the side AB,BC, CD and DA respectively.where    AB = 12cm and BC = 7cm. Also AJ = BK= CL= DM= x.The area of rectangle JKLM is 54cm2. Find x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17369 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=17369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE DRAWING BELOW<BR>\n" );
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document.write( "LET AK=BL=CM=DN=X<BR>\n" );
document.write( "AB=CD=12 AND BC=DA=7.<BR>\n" );
document.write( "FIRSTLY KLMN WILL NOT BE A RECTANGLE.IT WILL BE PARALLELOGRAM AS YOU CAN SEE BELOW.<BR>\n" );
document.write( "LET DC BE X AXIS AND DA BE Y AXIS WITH D AS ORIGIN.HENCE COORDINATES OF DIFFERENT POINTS ARE<BR>\n" );
document.write( "D...(0,0) M..(10,0) C…(12,0) L…(12,5) B….(12,7) K….(2,7) A….(0,7) N….(0,2)<BR>\n" );
document.write( "SLOPE OF MN =(0-2)/(10-0)= -1/5<BR>\n" );
document.write( "SLOPE OF NK =(7-2)/(2-0)= 5/2<BR>\n" );
document.write( "PRODUCT OF SLOPES =(-1/5)*((5/2)=-1/2…..SO THEY ARE NOT PERPENDICULAR.<BR>\n" );
document.write( "SO KLMN IS NOT A RECTANGLE.<BR>\n" );
document.write( "THEN FORMULA FOR AREA ALSO CHANGES.\r<BR>\n" );
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document.write( "LET US FIND AREAS OF 4 TRIANGLES AKN,KBL,LCM AND MDN ALL OF WHICH ARE RIGHT ANGLED TRIANGLES.<BR>\n" );
document.write( "SUM OF THEM IS 84-54=30..AS THIS IS EQUAL TO AREA OF ABCD(84) - AREA OF KLMN (54)<BR>\n" );
document.write( "SUM OF AREAS OF 4 TRIANGLES AKN,KBL,LCM AND MDN ARE<BR>\n" );
document.write( "(1/2){X(12-X)+X(7-X)+X(12-X)+X(7-X)}=X(12-X)+X(7-X)=X(12-X+7-X)=X(19-2X)=19X-2X^2=84-54=30<BR>\n" );
document.write( "2X^2-19X+30=0<BR>\n" );
document.write( "2X^2-4X-15X+30=0<BR>\n" );
document.write( "2X(X-2)-15(X-2)=0<BR>\n" );
document.write( "(X-2)(2X-15)=0<BR>\n" );
document.write( "X-2=0….OR……X=2<BR>\n" );
document.write( "2X-15=0….OR….X=7.5…WHICH IS BEYOND SIDES BC AND DA..SO NOT TO BE CONSIDERED.<BR>\n" );
document.write( "SO X=2 </SPAN>\n" );
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