document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204709>Question 1204709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Miss Allan has a piece of paper in the shape of a right-angled triangle<BR>\n" );
document.write( "𝐴𝐵𝐶 (with the right-angle at 𝐴). She folds vertex 𝐵 over onto the midpoint<BR>\n" );
document.write( "of 𝐴𝐶, then flattens the paper out to give a right-angled quadrilateral.<BR>\n" );
document.write( "What is the exact ratio of the area of this new quadrilateral to the area of<BR>\n" );
document.write( "the original triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841157 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3821)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hint:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0A%0D%0Acircle%28-2%2C-2%2C0.05%29%2Ccircle%28-2%2C-2%2C0.07%29%2Ccircle%28-2%2C-2%2C0.09%29%2Ccircle%28-2%2C-2%2C0.11%29%2Ccircle%28-2%2C-2%2C0.13%29%2Ccircle%28-2%2C-2%2C0.15%29%2Ccircle%28-2%2C-2%2C0.17%29%2Ccircle%28-2%2C-2%2C0.19%29%2Ccircle%28-2%2C3%2C0.05%29%2Ccircle%28-2%2C3%2C0.07%29%2Ccircle%28-2%2C3%2C0.09%29%2Ccircle%28-2%2C3%2C0.11%29%2Ccircle%28-2%2C3%2C0.13%29%2Ccircle%28-2%2C3%2C0.15%29%2Ccircle%28-2%2C3%2C0.17%29%2Ccircle%28-2%2C3%2C0.19%29%2Ccircle%282%2C-2%2C0.05%29%2Ccircle%282%2C-2%2C0.07%29%2Ccircle%282%2C-2%2C0.09%29%2Ccircle%282%2C-2%2C0.11%29%2Ccircle%282%2C-2%2C0.13%29%2Ccircle%282%2C-2%2C0.15%29%2Ccircle%282%2C-2%2C0.17%29%2Ccircle%282%2C-2%2C0.19%29%2Ccircle%280%2C-2%2C0.05%29%2Ccircle%280%2C-2%2C0.07%29%2Ccircle%280%2C-2%2C0.09%29%2Ccircle%280%2C-2%2C0.11%29%2Ccircle%280%2C-2%2C0.13%29%2Ccircle%280%2C-2%2C0.15%29%2Ccircle%280%2C-2%2C0.17%29%2Ccircle%280%2C-2%2C0.19%29%2Ccircle%28-2%2C0.5%2C0.05%29%2Ccircle%28-2%2C0.5%2C0.07%29%2Ccircle%28-2%2C0.5%2C0.09%29%2Ccircle%28-2%2C0.5%2C0.11%29%2Ccircle%28-2%2C0.5%2C0.13%29%2Ccircle%28-2%2C0.5%2C0.15%29%2Ccircle%28-2%2C0.5%2C0.17%29%2Ccircle%28-2%2C0.5%2C0.19%29%2Ccircle%280%2C0.5%2C0.05%29%2Ccircle%280%2C0.5%2C0.07%29%2Ccircle%280%2C0.5%2C0.09%29%2Ccircle%280%2C0.5%2C0.11%29%2Ccircle%280%2C0.5%2C0.13%29%2Ccircle%280%2C0.5%2C0.15%29%2Ccircle%280%2C0.5%2C0.17%29%2Ccircle%280%2C0.5%2C0.19%29%2C%0D%0A%0D%0Aline%28-2%2C-2%2C-2%2C3%29%2Cline%28-2%2C3%2C2%2C-2%29%2Cline%282%2C-2%2C-2%2C-2%29%2Cline%280%2C-2%2C-2%2C0.5%29%2Cline%280%2C-2%2C0%2C0.5%29%2Cline%28-2%2C0.5%2C0%2C0.5%29%2C%0D%0A%0D%0Aline%28-2%2C-1.65%2C-1.65%2C-1.65%29%2Cline%28-1.65%2C-1.65%2C-1.65%2C-2%29%2C%0D%0Aline%28-2%2C0.85%2C-1.65%2C0.85%29%2Cline%28-1.65%2C0.85%2C-1.65%2C0.5%29%2C%0D%0Aline%280%2C-1.65%2C0.35%2C-1.65%29%2Cline%280.35%2C-1.65%2C0.35%2C-2%29%2C%0D%0Aline%28-0.35%2C0.5%2C-0.35%2C0.15%29%2Cline%28-0.35%2C0.15%2C0%2C0.15%29%2C%0D%0A%0D%0A%0D%0Alocate%28-2.4%2C-2.22%2C%22A%22%29%2Clocate%28-2.58%2C3.22%2C%22B%22%29%2Clocate%281.96%2C-2.2%2C%22C%22%29%2Clocate%28-0.12%2C-2.2%2C%22D%22%29%2Clocate%28-2.32-0.1%2C0.66%2C%22E%22%29%2Clocate%280.32%2C0.64%2C%22F%22%29%0D%0A%0D%0A%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Right triangle ABC is folded over line EF to form trapezoid AEFC. <BR>\n" );
document.write( "Point B will move to point D. None of the other labeled points move.<BR>\n" );
document.write( "I recommend cutting out a piece of paper to do the fold yourself.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Some more hints<BR>\n" );
document.write( "AB = 2*AE<BR>\n" );
document.write( "AC = 2*EF<BR>\n" );
document.write( "E and F are midpoints of AB and BC respectively<BR>\n" );
document.write( "area of a triangle = 0.5*base*height<BR>\n" );
document.write( "area of a trapezoid = 0.5*height*(base1+base2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Technically the formulas aren't needed because there's an intuitive approach using the diagram shown above. But it doesn't hurt to use the formulas anyway.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Edit: The student has requested another hint. Notice how, based on the folds, we have 4 small congruent triangles. <BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );