document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199614>Question 199614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this question and sorry if it is kind of confusing since I cant get a picture (there is a equilateral triangle ABC i think i might be wrong but the two legs or sides are both 16 and i am supposed find the range that gives all possible values for b, and another one but same is that if the area of triangle ABC is 114 square units and h = 12, then calculate the value of b.)\r<BR>\n" );
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document.write( "thanks I am really sorry that this is really long,<BR>\n" );
document.write( "Craig  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150005 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If ABC is indeed an equilateral triangle, then all three sides must be equal (equi means equal, lateral means side).  Since your problem implies that there is a range to the value of the measure of the unspecified side, that means that you have an isosceles triangle, one that has two equal sides.\r<BR>\n" );
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document.write( "So, we know the sum of the lengths of the two sides you know is 16 + 16 = 32.  Now if your side <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> were any larger than 32, the two given sides would not stretch that far, and you would not have a triangle.  Also, if your side <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> measured exactly 32, then you would just have two straight lines on top of each other, and again you would not have a triangle.  But as long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b < 32\"> by any amount however small you have a triangle.  When <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> is very close to 32, you have a very wide but very short triangle.  As <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> gets smaller, the triangle gets narrower but taller.\r<BR>\n" );
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document.write( "Now, on the other end, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> has to measure something.  That is to say it can't be zero.  It can be very, very small giving you a very narrow but tall triangle.  So we can say that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b > 0\">\r<BR>\n" );
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document.write( "Putting all of that together, your range of values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0 < b < 32\">.\r<BR>\n" );
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document.write( "As to your second problem, you need to consider the formula for the area of a triangle given the base and height measures:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A = \frac{bh}{2}\">\r<BR>\n" );
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document.write( "But you are given the area and the height and wish to know the measure of the base, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ bh = 2A\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b = \frac{2A}{h}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b = \frac{2(114)}{12}\">\r<BR>\n" );
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document.write( "Just do the arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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