document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620095>Question 620095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of an equilateral triangle are given as x+3y,3x+2y-2 and 4x+1/2y+1 respectively.Find the lengths of the sides </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389984 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "To solve this problem, we will use the definition of an equilateral triangle. By definition, all three sides are equal in length. Using this fact, we can generate several equations. (NOTE: I assumed that the third side of the triangle has 1/2 as a coefficient of the y-term. It was difficult to tell what you meant; please make sure that I am solving the problem using the correct values. If not, email me and I'll make corrections.)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=3x%2B2y-2 ALIGN=MIDDLE  ALT=\"x%2B3y=3x%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B%281%2F2%29y%2B1=x%2B3y ALIGN=MIDDLE  ALT=\"4x%2B%281%2F2%29y%2B1=x%2B3y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B%281%2F2%29y%2B1=3x%2B2y-2 ALIGN=MIDDLE  ALT=\"4x%2B%281%2F2%29y%2B1=3x%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can use any two of the equations above to solve the problem. In essence, we want a value of x and y which are true for both equations. Let's use the first two equations. (It doesn't matter which two you choose.)<BR>\n" );
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document.write( "Step I: Simplify the first equation into slope-intercept form (y=...). Subtract x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=3x%2B2y-2 ALIGN=MIDDLE  ALT=\"x%2B3y=3x%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=2x%2B2y-2 ALIGN=MIDDLE  ALT=\"3y=2x%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Subtract 2y from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-2 ALIGN=MIDDLE  ALT=\"y=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Step 2: Use the substitution Method to solve the system of equation. Substitute 2x-2 for y in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B%281%2F2%29y%2B1=x%2B3y ALIGN=MIDDLE  ALT=\"4x%2B%281%2F2%29y%2B1=x%2B3y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B%281%2F2%29%282x-2%29%2B1%29=x%2B3%282x-2%29 ALIGN=MIDDLE  ALT=\"4x%2B%281%2F2%29%282x-2%29%2B1%29=x%2B3%282x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify by combining like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2Bx-1%2B1=x%2B6x-6%29 ALIGN=MIDDLE  ALT=\"4x%2Bx-1%2B1=x%2B6x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=7x-6 ALIGN=MIDDLE  ALT=\"5x=7x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=6 ALIGN=MIDDLE  ALT=\"2x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 3 for x in the first equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=3x%2B2y-2 ALIGN=MIDDLE  ALT=\"x%2B3y=3x%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B3y=3%283%29%2B2y-2 ALIGN=MIDDLE  ALT=\"3%2B3y=3%283%29%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Simplify by combining like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B3y=9%2B2y-2 ALIGN=MIDDLE  ALT=\"3%2B3y=9%2B2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "STEP III: Check your work.<BR>\n" );
document.write( "We have x=3 and y=4 as a solution to the system of equations. Since we have an equilateral triangle, these values should yield sides of equal length.<BR>\n" );
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document.write( "x+3y --> (3)+3(4)=3+12=15<BR>\n" );
document.write( "3x+2y-2 --> 3(3)+2(4)-2=9+8-2=15<BR>\n" );
document.write( "4x+(1/2)y+1 --> 4(3)+(1/2)(4)+1=12+2+1=15<BR>\n" );
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document.write( "Check, check, check! The three sides of the triangle each have length of 15 units.<BR>\n" );
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document.write( "Hope this helps. Feel free to email me if you have questions about this.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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