document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188247>Question 1188247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangle ABC is isosceles, with Line AB=AC, and Line BC=39 cm A square is inscribed in the triangle with edges 21 cm. Find the area of Triangle ADE\r<BR>\n" );
document.write( "\n" );
document.write( "Diagram: https://imgur.com/a/1RtmfbC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819293 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Triangles ADE and ABC are similar, and the similarity coefficient is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F39+=+7%2F13 ALIGN=MIDDLE  ALT=\"21%2F39+=+7%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the altitude of the triangle ADE;  then the altitude of the triangle ABC is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28h%2B21%29 ALIGN=MIDDLE  ALT=\"+%28h%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > centimeters.\r<BR>\n" );
document.write( "\n" );
document.write( "The ratio of altitudes is the same\r<BR>\n" );
document.write( "\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F%28h%2B21%29+=+7%2F13 ALIGN=MIDDLE  ALT=\"h%2F%28h%2B21%29+=+7%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It gives \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13h+=+7%2A%28h%2B21%29 ALIGN=MIDDLE  ALT=\"13h+=+7%2A%28h%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13h+=+7h+%2B+7%2A21 ALIGN=MIDDLE  ALT=\"13h+=+7h+%2B+7%2A21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13h+-+7h+=+147 ALIGN=MIDDLE  ALT=\"13h+-+7h+=+147\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6h+=+147 ALIGN=MIDDLE  ALT=\"6h+=+147\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+147%2F6 ALIGN=MIDDLE  ALT=\"h+=+147%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+24.5cm ALIGN=MIDDLE  ALT=\"h=+24.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Thus the height of the smaller triangle ADE is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=24.5cm ALIGN=MIDDLE  ALT=\"h=24.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  then the height of the larger triangle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B21=24.5%2B21+=+45.5cm ALIGN=MIDDLE  ALT=\"h%2B21=24.5%2B21+=+45.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now you know the base of the triangle ADE  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DE+=21cm ALIGN=MIDDLE  ALT=\"DE+=21cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and its height  of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=24.5cm ALIGN=MIDDLE  ALT=\"h=24.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, t hen its area of the smaller triangle ADE is  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%2A21cm%2A24.5cm+=+257.2cm%5E2+ ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%2A21cm%2A24.5cm+=+257.2cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );