document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149198>Question 1149198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram below, AGCD is a rectangle and GF=FC. Find the length of FE in cm. \r<BR>\n" );
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document.write( "Diagram: https://imgur.com/a/hzXoD2g </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770579 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are undoubtedly many different paths to the solution; here is what I came up with.<br><BR>\n" );
document.write( "AB = AD = 4, so extend DC to H so that ABHD is a square.  Extend AF to H, completing diagonal AH of the square.  Note triangle FCH is a 45-45-90 right triangle.<br><BR>\n" );
document.write( "Triangles ABE and HCE are similar; because CH = 2 and AB = 4, the ratio of similarity is 1:2.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EH%2FEA+=+1%2F2 ALIGN=MIDDLE  ALT=\"EH%2FEA+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EH%2FAH+=+1%2F3 ALIGN=MIDDLE  ALT=\"EH%2FAH+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AH+=+4%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"AH+=+4%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EH+=+%281%2F3%29AH+=+%284%2F3%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"EH+=+%281%2F3%29AH+=+%284%2F3%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FH+=+2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"FH+=+2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF+=+FH-EH+=+%282%2F3%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"EF+=+FH-EH+=+%282%2F3%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );