document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107833>Question 1107833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm a student of MSciEd secondary math.. I just wanna ask if you could answer the problem set that my instructor in mathed 235 haave given us.. the question is<BR>\n" );
document.write( "Let ABCD be trapezoid with the sides AD and BC parallel to each other and perpendicular to AB. moreover, assume that BC=2AD. the points P and Q on the side of AB divide it into three equal segments, and P is between A and Q. Similarly, the points R and S on the side of CD divide it into three equal segments, and R is between D and S. Let a1 be the area of the triangle, triangle AQR and let a2 be the area of the triangle, triangle PBS. Find the ratio a1/a2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722972 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++drawing%28400%2C400%2C+-2%2C+10%2C+-2%2C+10%2C%0D%0A+++++++++++line%28-2%2C0%2C10%2C0%29%2C%0D%0A+++++++++++line%280%2C-2%2C0%2C10%29%2C%0D%0A+++++++++++line%280%2C+4%2C+4%2C+4%29%2C%0D%0A++++++++++locate%28-0.5%2C4.3%2C+A%29%2C%0D%0A++++++++++locate%28-0.5%2C0%2C+B%29%2C%0D%0A++++++++++locate%284.5%2C4.3%2C+D%29%2C%0D%0A++++++++++locate%288.3%2C0%2C+C%29%2C%0D%0A++++++++++locate%28-0.5%2C2.7%2C+P%29%2C%0D%0A++++++++++locate%28-0.5%2C1.3%2C+Q%29%2C%0D%0A++++++++++locate%285.5%2C3.0%2CR%29%2C%0D%0A++++++++++locate%286.8%2C1.6%2CS%29%2C%0D%0A++++++++++red%28line%280%2C4%2C5.3%2C2.7%29%29%2C%0D%0A++++++++++red%28line%285.3%2C2.7%2C0%2C1.3%29%29%2C%0D%0A++++++++++red%28line%280%2C1.3%2C0%2C4%29%29%2C%0D%0A++++++++++green%28line%280%2C0%2C+6.7%2C+1.3%29%29%2C%0D%0A++++++++++green%28line%286.7%2C+1.3%2C+0%2C+2.6%29%29%2C%0D%0A++++++++++green%28line%280%2C2.6%2C+0%2C+0%29%29%2C+%0D%0A+++++++++++++%0D%0A+++++++++++line%284%2C4%2C+8%2C+0%29%0D%0A%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Area a1 = area of AQR<BR>\n" );
document.write( "Area a2 = area of PBS<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Base_AQR = (2/3)AB<BR>\n" );
document.write( "Base_PBS = (2/3)AB<BR>\n" );
document.write( "—<BR>\n" );
document.write( "The heights are measured along a line parallel to the x-axis, and note that the projection of DR onto the x-axis has length equal to (1/3)AD, while the projection of SD onto the x-axis has length (2/3)AD.\r<BR>\n" );
document.write( "\n" );
document.write( "Height_AQR = AD + (1/3)AD = (4/3)AD     <BR>\n" );
document.write( "Height_PBS = AD + (2/3)AD = (5/3)AD\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--<BR>\n" );
document.write( "Area_a1 = (1/2) (2/3)AB * (4/3)AD<BR>\n" );
document.write( "Area_a2 = (1/2)  (2/3)AB * (5/3)AD<BR>\n" );
document.write( "—\r<BR>\n" );
document.write( "\n" );
document.write( "Answer:   Area_a1/Area_a2 =  <b>4/5</b>\r<BR>\n" );
document.write( "\n" );
document.write( "—\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );