document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=696621>Question 696621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> divide a right angled triangle of sides ab=77 feet is the base,bc=60 feet and ca=97 feet into four equal parts longitudinally.<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 #429266 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=429266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A triangle of sides AB=77 feet, BC=60 feet and CA=97 feet, does not have a right angle at B.<BR>\n" );
document.write( "A triangle of sides AB=77 feet, BC=59 feet and CA=97 feet, has an angle at C that is for practical purposes a right angle (not exactly, but you would not notice the difference).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.5%2C78.5%2C-10%2C70%2C%0D%0Atriangle%280%2C0%2C0%2C59%2C77%2C0%29%2Crectangle%280%2C0%2C3%2C3%29%2C%0D%0Alocate%2835%2C-1%2C77%29%2Clocate%281%2C30%2C59%29%2Clocate%2837%2C35%2C97%29%2C%0D%0Alocate%28-1%2C-1%2CB%29%2Clocate%2876%2C-1%2CA%29%2Clocate%28-1%2C65%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > We need to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.5%2C78.5%2C-10%2C70%2C%0D%0Atriangle%280%2C0%2C0%2C59%2C77%2C0%29%2Crectangle%280%2C0%2C3%2C3%29%2C%0D%0Arectangle%2810.5%2C0%2C13.5%2C3%29%2Crectangle%2822.6%2C0%2C25.6%2C3%29%2Crectangle%2838.5%2C0%2C41.5%2C3%29%2C%0D%0Agreen%28line%2810.5%2C-10%2C10.5%2C80%29%29%2Cgreen%28line%2822.6%2C-10%2C22.6%2C80%29%29%2C%0D%0Agreen%28line%2838.5%2C-10%2C38.5%2C80%29%29%2C%0D%0Alocate%28-1%2C-1%2CB%29%2Clocate%2876%2C-1%2CA%29%2Clocate%28-1%2C65%2CC%29%2C%0D%0Alocate%2812%2C-1%2CZ%29%2Clocate%2824%2C-1%2CY%29%2Clocate%2840%2C-1%2CX%29%2C%0D%0Alocate%2812%2C54%2CR%29%2Clocate%2824%2C44%2CQ%29%2Clocate%2840%2C32%2CP%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AXP%29=area%28XYQP%29=area%28YZRQ%29=area%28ZBCR%29=%281%2F4%29%2Aarea%28ABC%29 ALIGN=MIDDLE  ALT=\"area%28AXP%29=area%28XYQP%29=area%28YZRQ%29=area%28ZBCR%29=%281%2F4%29%2Aarea%28ABC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "AXP and ABC are similar right triangles.<BR>\n" );
document.write( "PA and CA are the corresponding longest sides of each triangle;<BR>\n" );
document.write( "XP and BC are the corresponding shortest sides, and]=<BR>\n" );
document.write( "AX and AB are corresponding sides too.\r<BR>\n" );
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document.write( "In similar triangles, the ratio of the areas equals the ratio of the lengths of the corresponding sides, squared.<BR>\n" );
document.write( "In math equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28ABC%29%2Farea%28AXP%29=%28AB%2FAX%29%5E2 ALIGN=MIDDLE  ALT=\"area%28ABC%29%2Farea%28AXP%29=%28AB%2FAX%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AXP%29=%281%2F4%29%2Aarea%28ABC%29 ALIGN=MIDDLE  ALT=\"area%28AXP%29=%281%2F4%29%2Aarea%28ABC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AXP%29%2Farea%28ABC%29=%281%2F4%29 ALIGN=MIDDLE  ALT=\"area%28AXP%29%2Farea%28ABC%29=%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28ABC%29%2Farea%28AXP%29=4 ALIGN=MIDDLE  ALT=\"area%28ABC%29%2Farea%28AXP%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%2FAX%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28AB%2FAX%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2FAX=sqrt%284%29=2 ALIGN=MIDDLE  ALT=\"AB%2FAX=sqrt%284%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AX%2FAB%29%5E2=1%2F4 ALIGN=MIDDLE  ALT=\"%28AX%2FAB%29%5E2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AX%2FAB=sqrt%281%2F4%29=1%2F2 ALIGN=MIDDLE  ALT=\"AX%2FAB=sqrt%281%2F4%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, if AB=77 feet, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AX=%281%2F2%29AB=%281%2F2%29%2A77 ALIGN=MIDDLE  ALT=\"AX=%281%2F2%29AB=%281%2F2%29%2A77\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AX=38.5 ALIGN=MIDDLE  ALT=\"AX=38.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft<BR>\n" );
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document.write( "If you look hard enough you will see that there are 4 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28similar%29 ALIGN=MIDDLE  ALT=\"highlight%28similar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > right triangles with a vertex at A:<BR>\n" );
document.write( "ABC, AZR, AYQ, and AXP.<BR>\n" );
document.write( "How are their areas related?<BR>\n" );
document.write( "ABC is split into its 4 pieces of area equal to the area of AXP.<BR>\n" );
document.write( "AYQ contains 2 of those pieces, and AZR contains 3.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AYQ%29=2%2Aarea%28AXP%29 ALIGN=MIDDLE  ALT=\"area%28AYQ%29=2%2Aarea%28AXP%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AYQ%29%2Farea%28AXP%29=2 ALIGN=MIDDLE  ALT=\"area%28AYQ%29%2Farea%28AXP%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AZR%29=3%2Aarea%28AXP%29 ALIGN=MIDDLE  ALT=\"area%28AZR%29=3%2Aarea%28AXP%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area%28AZR%29%2Farea%28AXP%29=3 ALIGN=MIDDLE  ALT=\"area%28AZR%29%2Farea%28AXP%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using again the fact that the ratio of areas equals the ratio of the lengths of the corresponding sides, squared,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AY%2FAX%29%5E2=2 ALIGN=MIDDLE  ALT=\"%28AY%2FAX%29%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AY%2FAX=sqrt%282%29 ALIGN=MIDDLE  ALT=\"AY%2FAX=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AY=sqrt%282%29%2AAX ALIGN=MIDDLE  ALT=\"AY=sqrt%282%29%2AAX\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AY=38.5sqrt%282%29 ALIGN=MIDDLE  ALT=\"AY=38.5sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2854.4%29 ALIGN=MIDDLE  ALT=\"highlight%2854.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AZ%2FAX%29%5E2=3 ALIGN=MIDDLE  ALT=\"%28AZ%2FAX%29%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AZ%2FAX=sqrt%283%29 ALIGN=MIDDLE  ALT=\"AZ%2FAX=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AZ=sqrt%283%29%2AAX ALIGN=MIDDLE  ALT=\"AZ=sqrt%283%29%2AAX\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AZ=38.5sqrt%283%29 ALIGN=MIDDLE  ALT=\"AZ=38.5sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2866.7%29 ALIGN=MIDDLE  ALT=\"highlight%2866.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet </SPAN>\n" );
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