document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979057>Question 979057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a right angle triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hyootenuse into segment which are 10 cm and 6 cm long. Find the lengths of the two sides of the triangle.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600470 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=600470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a right triangle, the altitude to the hypotenuse splits the triangle into two smaller right triangles, and you end up with three similar right triangles<BR>\n" );
document.write( "As a consequence, there is a bunch of proportions between the lengths of the sides of those triangles that are useful to solve this problem.<BR>\n" );
document.write( "You may even have had to memorize some formulas/theorems based on that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-1%2C17%2C-1.5%2C7.5%2C%0D%0Atriangle+%280%2C0%2C4%2C0%2C4%2C6.93%29%2Ctriangle+%280%2C0%2C16%2C0%2C4%2C6.93%29%2C%0D%0Arectangle%284%2C0%2C4.5%2C0.5%29%2Clocate%287.85%2C-0.1%2Ca%29%2C%0D%0Aarrow%287.7%2C-0.5%2C0%2C-0.5%29%2Carrow%288.3%2C-0.5%2C16%2C-0.5%29%2C%0D%0Alocate%281.9%2C0.7%2Cd%29%2Clocate%289.9%2C0.7%2Ce%29%2C%0D%0Alocate%282%2C3.45%2Cb%29%2Clocate%289.5%2C3.45%2Cc%29%2Clocate%284.1%2C3.5%2Ch%29%2C%0D%0Aline%283.75%2C6.5%2C4.18%2C6.25%29%2Cline%284.43%2C6.68%2C4.18%2C6.25%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa=d%2Fb ALIGN=MIDDLE  ALT=\"b%2Fa=d%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=ad ALIGN=MIDDLE  ALT=\"b%5E2=ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa=e%2Fc ALIGN=MIDDLE  ALT=\"c%2Fa=e%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=ae ALIGN=MIDDLE  ALT=\"c%5E2=ae\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In this problem there is another perpendicular to the hypotenuse, like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-1%2C17%2C-1.5%2C7.5%2C%0D%0Atriangle+%280%2C0%2C4%2C0%2C4%2C6.93%29%2Ctriangle+%280%2C0%2C16%2C0%2C4%2C6.93%29%2C%0D%0Arectangle%284%2C0%2C4.5%2C0.5%29%2Ctriangle+%2810%2C0%2C16%2C0%2C10%2C3.465%29%2C%0D%0Arectangle%2810%2C0%2C10.5%2C0.5%29%2Clocate%287.85%2C-0.6%2Ca%29%2C%0D%0Aarrow%287.7%2C-1%2C0%2C-1%29%2Carrow%288.3%2C-1%2C16%2C-1%29%2C%0D%0Alocate%281.9%2C0.7%2Cd%29%2Clocate%282%2C3.45%2Cb%29%2C%0D%0Alocate%2812%2C2.3%2Cc%2F2%29%2Clocate%286.8%2C5.2%2Cc%2F2%29%2C%0D%0Alocate%284.05%2C3.5%2Ch%29%2C%0D%0Alocate%2812.3%2C0%2C%22e%2F2%22%29%2Clocate%286.3%2C0%2C%22e%2F2%22%29%2C%0D%0Aline%283.75%2C6.5%2C4.18%2C6.25%29%2Cline%284.43%2C6.68%2C4.18%2C6.25%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That perpendicular is splitting in half the hypotenuse and one leg of one of the smaller triangles.<BR>\n" );
document.write( "In the problem  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10cm%2B6cm=16cm ALIGN=MIDDLE  ALT=\"a=10cm%2B6cm=16cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and it must be that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%2F2=6cm ALIGN=MIDDLE  ALT=\"e%2F2=6cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=2%2A6cm=12cm ALIGN=MIDDLE  ALT=\"e=2%2A6cm=12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%2F2=10cm ALIGN=MIDDLE  ALT=\"e%2F2=10cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=20cm%3E16cm=a ALIGN=MIDDLE  ALT=\"e=20cm%3E16cm=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not make sense.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=12cm ALIGN=MIDDLE  ALT=\"e=12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=a-e=16cm%2B12cm=4cm ALIGN=MIDDLE  ALT=\"d=a-e=16cm%2B12cm=4cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the proportions above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=ad ALIGN=MIDDLE  ALT=\"b%5E2=ad\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%28ad%29=sqrt%28%2816cm%29%284cm%29%29=sqrt%2864cm%5E2%29=highlight%288cm%29 ALIGN=MIDDLE  ALT=\"b=sqrt%28ad%29=sqrt%28%2816cm%29%284cm%29%29=sqrt%2864cm%5E2%29=highlight%288cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=ae ALIGN=MIDDLE  ALT=\"c%5E2=ae\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28ae%29=sqrt%28%2816cm%29%2812cm%29%29=sqrt%28192cm%5E2%29=highlight%28sqrt%283%29cm%29=about13.86cm ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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