document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=568183>Question 568183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the triangle y/x = 3. Which one of the following must be true?<BR>\n" );
document.write( "a. 4x>z<BR>\n" );
document.write( "b. 4x < z<BR>\n" );
document.write( "c. 4x=z<BR>\n" );
document.write( "d. it cannot be determined from the information given\r<BR>\n" );
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document.write( "The picture of the triangle shows one side is X one side is Y and one side is Z.<BR>\n" );
document.write( "There is no right angle.the xy angle is obtuse, the zy and xz angles are acute.\r<BR>\n" );
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document.write( "I wish I knew how to draw the triangle for you but hopefully my description will do it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366866 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=366866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the way to analyze the situation.  Since Z is opposite of the obtuse (biggest) angle, Z must be the longest side of the triangle. (This should be obvious from the drawing you were given for the triangle.)<BR>\n" );
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document.write( "That means that the SUM of lengths of the two sides labeled X and Y must be greater than Z. (I believe that this is a theorem or an axiom.) Why is that true? Think about this. You cannot form a triangle if the lengths X and Y when added together are less than or just equal to the length of Z. If you need help picturing this, make this drawing: <BR>\n" );
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document.write( "A. Draw a 4 inch long line about in the center of a sheet of paper. <BR>\n" );
document.write( "B. Take a drawing compass and set the distance between its point and lead tip at 2 inches.<BR>\n" );
document.write( "C. Place the compass point at one end of the 4 inch line swing a circle (of 2 inch radius) around that end of the line.<BR>\n" );
document.write( "D. Then reset drawing compass so that the distance between its point and lead tip is 1 inch.<BR>\n" );
document.write( "E. This time set the compass point at the other end of the 4 inch line and swing a circle (of 1 inch radius) around this end of the 4 inch line.\r<BR>\n" );
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document.write( "Notice that this is the case where the lengths of the two short sides (2 inch and 1 inch) total less than the long side (4 inches). The circles do not intersect meaning that the proposed length of 2 inches and 1 inch cannot be joined to form a triangle. If the radii of the two circles added up to be bigger than the longest side (for example one circle of radius 3 and the other of radius 2) then the circles would intersect and a triangle could be formed by drawing lines from the ends of the 4 inch line to the point where the circles intersected. One line to the intersection would be 3 units long and the other line would be 2 inches long, making a triangle of sides 2, 3, and 4.<BR>\n" );
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document.write( "Once you can visualize and are convinced that X + Y has to be greater than Z for a triangle to be formed, you can write the inequality for a triangle having Z as its long side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+Y+%3E+Z ALIGN=MIDDLE  ALT=\"X+%2B+Y+%3E+Z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then you are told in the problem that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%2FX+=3 ALIGN=MIDDLE  ALT=\"Y%2FX+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this given equation for Y in terms of X by multiplying both sides by X to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=3X ALIGN=MIDDLE  ALT=\"Y+=3X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now go to the inequality that we wrote above and in place of Y substitute its equal 3X to make the inequality become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+3X+%3E+Z ALIGN=MIDDLE  ALT=\"X+%2B+3X+%3E+Z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the two terms on the left side and you have the requirement that in the given triangle:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4X+%3E+Z ALIGN=MIDDLE  ALT=\"4X+%3E+Z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is answer a. in the list of answers that you were given.<BR>\n" );
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document.write( "I hope this helps you to understand the problem that you were given and gives you a little more insight into how triangles are formed.<BR>\n" );
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document.write( " </SPAN>\n" );
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