document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74137>Question 74137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the length x in each triangle. Express your answer in simplified radical form. \r<BR>\n" );
document.write( "\n" );
document.write( "Side 1: 10  Side 2: 8 Bottom: x\r<BR>\n" );
document.write( "\n" );
document.write( "I need some help with this problem. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53136 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to guess that the triangle you were given is a right triangle (one of the angles is<BR>\n" );
document.write( "90 degrees and the two shortest sides meet to form that 90 degree angle). The longest<BR>\n" );
document.write( "side is called the hypotenuse and it is likely to be side 1 (length 10) in the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If this is the case, then we can use a rule called the Pythagorean theorem which says that<BR>\n" );
document.write( "\"the sum of the squares of the two legs (short sides) of a right triangle are equal to<BR>\n" );
document.write( "the square of the hypotenuse (longest side).  In equation form this would be:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now all we have to do is substitute your given values into this equation.  c is the long<BR>\n" );
document.write( "side and, as I view your problem, is 10. So substitute 10 for c and the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "One of the short sides is known to be 8. It doesn't matter whether we call it b or a. Either<BR>\n" );
document.write( "one will work.  So lets call it b as long as there's no difference.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute 8 for b and the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+8%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+8%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then let's substitute x for \"a\" so that the unknown side matches what the problem calls it.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2+=+64 ALIGN=MIDDLE  ALT=\"8%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+100 ALIGN=MIDDLE  ALT=\"10%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > so let's substitute those two values to<BR>\n" );
document.write( "get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+64+=+100 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+64+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then eliminate the 64 on the left side by subtracting 64 from both sides.  When you do that <BR>\n" );
document.write( "the equation reduces to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+36 ALIGN=MIDDLE  ALT=\"x%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can solve this equation for “a” by taking the square root of both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29+=+sqrt%2836%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29+=+sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And this simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<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( ".<BR>\n" );
document.write( "That’s the answer for this triangle.  The side you are missing has to be the shortest side <BR>\n" );
document.write( "and it is 6 units long.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I hope that I was right in guessing that you were dealing with a right triangle. If it's not<BR>\n" );
document.write( "the case, then I apologize, and you'll have to post again with more information about the<BR>\n" );
document.write( "triangle so that a tutor can understand what the triangle looks like. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "In either case, I hope that you gain an understanding of the use of the Pythagorean theorem.  <BR>\n" );
document.write( "The Pythagorean theorem ONLY works on RIGHT triangles so don’t try to use it on just any <BR>\n" );
document.write( "old triangle that comes along.  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );