document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189025>Question 1189025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ΔABC is an isosceles right triangle with AC=4√3. F is the mid-point of hypotenuse  AC, and ΔDEF is equilateral. Find the perimeter of ΔDEF. <BR>\n" );
document.write( "A) 6(3 - √3)   B) 6(2 - √3)   C) 6(5 - 2√3)   D) 3(3 - √3)   E) 4(5 - 2√3)<BR>\n" );
document.write( "https://ibb.co/Vgvz8RG     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820243 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=820243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-1%2C7%2C-1%2C7%0D%0A%2Cline%280%2C0%2C4.9%2C0%29%2Cline%280%2C0%2C0%2C4.9%29%2Cline%284.9%2C0%2C0%2C4.9%29%0D%0A%2Cline%281.79%2C0%2C2.45%2C2.45%29%2Cline%280%2C1.79%2C2.45%2C2.45%29%2Cline%281.79%2C0%2C0%2C1.79%29%0D%0A%2Clocate%28-.2%2C4.9%2CA%29%2Clocate%280%2C0%2CB%29%2Clocate%284.9%2C0%2CC%29%2Clocate%28-.2%2C1.79%2CD%29%2Clocate%281.79%2C0%2CE%29%2Clocate%282.65%2C2.45%2CF%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "AC=4*sqrt(3)<BR>\n" );
document.write( "F is the midpoint of AC, so AF=FC=2*sqrt(3)<BR>\n" );
document.write( "DEF is equilateral<br><BR>\n" );
document.write( "To find: The perimeter of DEF<br><BR>\n" );
document.write( "Draw BF intersecting DE at G:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-1%2C7%2C-1%2C7%0D%0A%2Cline%280%2C0%2C4.9%2C0%29%2Cline%280%2C0%2C0%2C4.9%29%2Cline%284.9%2C0%2C0%2C4.9%29%0D%0A%2Cline%281.79%2C0%2C2.45%2C2.45%29%2Cline%280%2C1.79%2C2.45%2C2.45%29%2Cline%281.79%2C0%2C0%2C1.79%29%0D%0A%2Cred%28line%280%2C0%2C2.45%2C2.45%29%29%0D%0A%2Clocate%28-.2%2C4.9%2CA%29%2Clocate%280%2C0%2CB%29%2Clocate%284.9%2C0%2CC%29%2Clocate%28-.2%2C1.79%2CD%29%2Clocate%281.79%2C0%2CE%29%2Clocate%282.65%2C2.45%2CF%29%0D%0A%2Cred%28locate%281%2C1%2CG%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "BF bisects DE; and the length of BF is 2*sqrt(3) -- same as AF and FC.<br><BR>\n" );
document.write( "BF divides DEF into two 30-60-90 right triangles.<br><BR>\n" );
document.write( "Let x be the length of EG; then the side length of DEF is 2x, and FG is x*sqrt(3).<br><BR>\n" );
document.write( "BGE is an isosceles right triangle, so the length of BG is also x.<br><BR>\n" );
document.write( "Now we have BF = BG+GF:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29=x%2Bx%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29=x%2Bx%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29=x%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29=x%281%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29%2F%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29%2F%281%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2Asqrt%283%29%29%281-sqrt%283%29%29%2F%28%281%2Bsqrt%283%29%29%281-sqrt%283%29%29%29 ALIGN=MIDDLE  ALT=\"x=%282%2Asqrt%283%29%29%281-sqrt%283%29%29%2F%28%281%2Bsqrt%283%29%29%281-sqrt%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2Asqrt%283%29-6%29%2F%281-3%29+=+%286-2%2Asqrt%283%29%29%2F2+=+3-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=%282%2Asqrt%283%29-6%29%2F%281-3%29+=+%286-2%2Asqrt%283%29%29%2F2+=+3-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Finally, the perimeter of DEF is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=6%283-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"6x=6%283-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: A <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"6%283-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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