document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=833510>Question 833510</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five lines parallel to the base of a triangle divide the other sides of the triangle each into 6 equal segments and the area into 6 distinct parts. If the area of the largest of these parts is 66 cm squared then the area of the original triangle is:\r<BR>\n" );
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document.write( "I have drawn this out and played around with the lines but I do not see how I can find the area of any of the 6 sections </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502614 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=502614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each section plus everything above that section base is a triangle.<BR>\n" );
document.write( "They are all similar triangles with the side lengths in the proportion<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221+%3A+2+%3A+3+%3A+4+%3A+5+%3A+6%22 ALIGN=MIDDLE  ALT=\"%221+%3A+2+%3A+3+%3A+4+%3A+5+%3A+6%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The length of base and height are also in the same proportion, of course.<BR>\n" );
document.write( "So, the areas are in the proportion<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2%3A2%5E2%3A3%5E2%3A4%5E2%3A5%5E2%3A6%5E2=1%3A4%3A9%3A16%3A25%3A36 ALIGN=MIDDLE  ALT=\"1%5E2%3A2%5E2%3A3%5E2%3A4%5E2%3A5%5E2%3A6%5E2=1%3A4%3A9%3A16%3A25%3A36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the triangle made up of the top two sections is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the smallest (top) triangle.<BR>\n" );
document.write( "The area of the triangle made up of the top three sections is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the smallest (top) triangle.<BR>\n" );
document.write( "The area of the triangle made up of the top four sections is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the smallest (top) triangle.<BR>\n" );
document.write( "The area of the triangle made up of the top five sections is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the smallest (top) triangle.<BR>\n" );
document.write( "The original triangle's area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the area of the smallest (top) triangle.<BR>\n" );
document.write( "Let's call the area of the smallest (top) triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > square centimeters.<BR>\n" );
document.write( "The area of the triangle made up of the top five sections is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x ALIGN=MIDDLE  ALT=\"25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > square centimeters.<BR>\n" );
document.write( "The original triangle's area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x ALIGN=MIDDLE  ALT=\"36x\"   DISABLED_style= \"max-width:90%; height:auto;\" > square centimeters.<BR>\n" );
document.write( "The difference, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x-25x=11x ALIGN=MIDDLE  ALT=\"36x-25x=11x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , is the area, in square centimeters of the bottom section.<BR>\n" );
document.write( "Our equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x=66 ALIGN=MIDDLE  ALT=\"11x=66\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=66%2F11 ALIGN=MIDDLE  ALT=\"x=66%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The area of the original triangle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x=36%2A6=highlight%28216%29 ALIGN=MIDDLE  ALT=\"36x=36%2A6=highlight%28216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > square centimeters.<BR>\n" );
document.write( " <BR>\n" );
document.write( "A picture is worth a thousand words:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C7%2C-1%2C7%2C%0D%0Atriangle%280%2C0%2C6%2C0%2C4%2C6%29%2C%0D%0Ared%28line%28-0.5%2C1%2C6.5%2C1%29%29%2Cred%28line%28-0.5%2C2%2C6.5%2C2%29%29%2C%0D%0Ared%28line%28-0.5%2C3%2C6.5%2C3%29%29%2Cred%28line%28-0.5%2C4%2C6.5%2C4%29%29%2C%0D%0Ared%28line%28-0.5%2C5%2C6.5%2C5%29%29%2Cgreen%28line%281%2C0%2C4.33%2C5%29%29%2C%0D%0Agreen%28line%282%2C0%2C4.67%2C4%29%29%2Cgreen%28line%283%2C0%2C5%2C3%29%29%2C%0D%0Agreen%28line%284%2C0%2C5.33%2C2%29%29%2Cgreen%28line%285%2C0%2C5.67%2C1%29%29%2C%0D%0Agreen%28line%281%2C0%2C0.67%2C1%29%29%2Cgreen%28line%282%2C0%2C1.33%2C2%29%29%2C%0D%0Agreen%28line%284%2C0%2C2.67%2C4%29%29%2Cgreen%28line%283%2C0%2C2%2C3%29%29%2C%0D%0Agreen%28line%285%2C0%2C3.33%2C5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > I added green lines to split the whole thing into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangles that are congruent with (the same as) the smallest (top) triangle.<BR>\n" );
document.write( "Do you see hoe there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > small triangles in all and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them in the bottom section? </SPAN>\n" );
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