document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193077>Question 1193077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> M and N are the midpoints of sides <BR>\n" );
document.write( "RS and RT of △RST, respectively.<BR>\n" );
document.write( "Given:	<BR>\n" );
document.write( "RM = RN = 3x + 1<BR>\n" );
document.write( "ST = 7x − 2<BR>\n" );
document.write( "m∠R = 60°<BR>\n" );
document.write( "Find:	<BR>\n" );
document.write( "x, RM, and ST </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825028 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Given: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RM+=+RN+=+3x+%2B+1 ALIGN=MIDDLE  ALT=\"RM+=+RN+=+3x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST+=+7x+-+2 ALIGN=MIDDLE  ALT=\"ST+=+7x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+60 ALIGN=MIDDLE  ALT=\"R+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "Find: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RM ALIGN=MIDDLE  ALT=\"RM\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST ALIGN=MIDDLE  ALT=\"ST\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you draw the triangle and label the sides you will see that the smaller triangle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+RMN ALIGN=MIDDLE  ALT=\"+RMN\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an isosceles triangle because two of its sides are equal. So the base angles have to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=congruent ALIGN=MIDDLE  ALT=\"congruent\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "we can find the missing angles because we have measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+60 ALIGN=MIDDLE  ALT=\"R+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we know that sum of interior angles in a triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RMN ALIGN=MIDDLE  ALT=\"RMN\"   DISABLED_style= \"max-width:90%; height:auto;\" >= measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RNM=+%28180-60%29%2F2=60 ALIGN=MIDDLE  ALT=\"RNM=+%28180-60%29%2F2=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you will see that all the three angles in triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RMN ALIGN=MIDDLE  ALT=\"RMN\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > each. \r<BR>\n" );
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document.write( "So it is an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equilateral ALIGN=MIDDLE  ALT=\"equilateral\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangle. \r<BR>\n" );
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document.write( "Then the 3rd side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the first two sides<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+RM ALIGN=MIDDLE  ALT=\"+RM\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RN ALIGN=MIDDLE  ALT=\"RN\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "so we now have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN=+4x+%2B1 ALIGN=MIDDLE  ALT=\"MN=+4x+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using triangle mid segment theorem, we know that the midsegment <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( line connecting the midpoints of two sides of a triangle is midsegment) is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST ALIGN=MIDDLE  ALT=\"ST\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it’s length is half of the length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST ALIGN=MIDDLE  ALT=\"ST\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN+=++ST%2F2 ALIGN=MIDDLE  ALT=\"MN+=++ST%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST+=+2+MN ALIGN=MIDDLE  ALT=\"ST+=+2+MN\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
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document.write( "plug in the values\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+-2+=+2%283x+%2B+1%29 ALIGN=MIDDLE  ALT=\"7x+-2+=+2%283x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+-2+=+6x+%2B+6 ALIGN=MIDDLE  ALT=\"7x+-2+=+6x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+-6x+=+2+%2B+6 ALIGN=MIDDLE  ALT=\"7x+-6x+=+2+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RM+=+3%2A8+%2B+1=25 ALIGN=MIDDLE  ALT=\"RM+=+3%2A8+%2B+1=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ST+=+7%2A8+-+2=54 ALIGN=MIDDLE  ALT=\"ST+=+7%2A8+-+2=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );