document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704266>Question 704266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if there is a triangle, the measurements of the three sides are 6, 8, and 10. what is the altitude of the triangle? it says to write a proportion and solve for x(the altitude). please help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434053 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=434053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An altitude of a triangle is a segment perpendicular to a side going from that side to the opposite vertex,<BR>\n" );
document.write( "Because a triangle has 3 sides, there are 3 altitudes.<BR>\n" );
document.write( "That particular triangle (as all triangles with side lengths in the ratio 3:4:5) is a right triangle.<BR>\n" );
document.write( "Two of the altitudes are the legs of the right triangle (the shorter, perpendicular sides).<BR>\n" );
document.write( "Each one is the altitude perpendicular to the other one.<BR>\n" );
document.write( "We have to assume they want the other altitude, the one going from the side measuring 10 to the right angle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-1%2C11%2C-2%2C6%2C%0D%0Atriangle%280%2C0%2C10%2C0%2C5.5%2C4.8%29%2C%0D%0Agreen%28line%285.5%2C0%2C5.5%2C4.8%29%29%2Cgreen%28rectangle%285.5%2C0%2C5.2%2C0.3%29%29%2C%0D%0Alocate%285.6%2C2.5%2Cgreen%28x%29%29%2Clocate%284.7%2C-0.2%2C10%29%2C%0D%0Aarrow%284.5%2C-0.5%2C0%2C-0.5%29%2C+arrow%285.5%2C-0.5%2C10%2C-0.5%29%2C%0D%0Alocate%282.6%2C3%2C8%29%2Clocate%287.7%2C3%2C6%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > If you are supposed to realize that it is a right triangle,<BR>\n" );
document.write( "you would conclude that the altitude divides the triangle into two similar triangles.<BR>\n" );
document.write( "The pieces are similar to the original, larger right triangle, <BR>\n" );
document.write( "because they have a pair of congruent right angles,<BR>\n" );
document.write( "and a \"pair\" of congruent acute angles<BR>\n" );
document.write( "(that are really the same angle shared by the original triangle and its smaller triangular piece).<BR>\n" );
document.write( "In the original triangle, the angle at bottom right,<BR>\n" );
document.write( "opposite the longer leg measuring 8, <BR>\n" );
document.write( "is the larger of the acute angles,<BR>\n" );
document.write( "and it is shared with the smaller triangle,<BR>\n" );
document.write( "where it is opposite the small triangle's longer leg, which measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then, you could write proportions involving the length of corresponding sides in similar triangles.<BR>\n" );
document.write( "For example, you could state that the ratio of long leg to hypotenuse is the same for the original triangle as for the smaller piece by writing the proportion<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6=8%2F10 ALIGN=MIDDLE  ALT=\"x%2F6=8%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which can be solved by multiplying both sides of the equal sign times 6 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2A8%2F10 ALIGN=MIDDLE  ALT=\"x=6%2A8%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=24%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=24%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4.8%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If you are not supposed to realize that it is a right triangle,<BR>\n" );
document.write( "you would not know that the triangles are similar, and would not be able to write the proportion as above. It may get complicated.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Of course, if you realized it was a right triangle, and you did not think about a proportion, you may calculate area of the triangle taking length of one leg as base, and the other as height as<BR>\n" );
document.write( "area =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A8%2F2=48%2F2 ALIGN=MIDDLE  ALT=\"6%2A8%2F2=48%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and knowing that also area =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2F2 ALIGN=MIDDLE  ALT=\"10x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would figure out than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x=48 ALIGN=MIDDLE  ALT=\"10x=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > qnd <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=48%2F10 ALIGN=MIDDLE  ALT=\"x=48%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.8 ALIGN=MIDDLE  ALT=\"x=4.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );