document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618657>Question 618657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the ratio of two sides of a parallelogram is 3:5 and its perimeter is 48cm. find the sides of the parallelogram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389070 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=389070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Recall that a parallelogram has two pairs of parallel sides. We will use two variables to solve this problem.<BR>\n" );
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document.write( "Let x be the length of each of the shorter pair of parallel sides.<BR>\n" );
document.write( "Let y be the length of each of the longer pair of parallel sides.<BR>\n" );
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document.write( "We will use the information given in the problem to write two equations that model the problem. The perimeter (48 cm.) is the sum of the four sides, so<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48=x%2Bx%2By%2By ALIGN=MIDDLE  ALT=\"48=x%2Bx%2By%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=48 ALIGN=MIDDLE  ALT=\"2x%2B2y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The ratio of two sides of the parallelogram is 3:5. Since the parallel sides of a parallelogram have equal length, we know that we are comparing the lengths x and y here, so<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy=3%2F5 ALIGN=MIDDLE  ALT=\"x%2Fy=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "NOTE: We set up the variables so that x is shorter than y. So \"x is to y as 3 is to 5.\"<BR>\n" );
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document.write( "Now we have two variables and two equations. We can solve the system to find the values of x and y.<BR>\n" );
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document.write( "Rewrite the first equation in terms of x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=48 ALIGN=MIDDLE  ALT=\"2x%2B2y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=48-2x ALIGN=MIDDLE  ALT=\"2y=48-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24-x ALIGN=MIDDLE  ALT=\"y=24-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 24-x for y in the second equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy=3%2F5 ALIGN=MIDDLE  ALT=\"x%2Fy=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%2824-x%29=3%2F5 ALIGN=MIDDLE  ALT=\"x%2F%2824-x%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x. I will skip a bunch of algebra steps and cross-multiply.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=3%2824-x%29 ALIGN=MIDDLE  ALT=\"5x=3%2824-x%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=72-3x ALIGN=MIDDLE  ALT=\"5x=72-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=72 ALIGN=MIDDLE  ALT=\"8x=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We now know that the shorter sides have a length of 9 cm. Substitute 9 for x in the first equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=48 ALIGN=MIDDLE  ALT=\"2x%2B2y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%289%29%2B2y=48 ALIGN=MIDDLE  ALT=\"2%289%29%2B2y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2B2y=48 ALIGN=MIDDLE  ALT=\"18%2B2y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=48-18=30 ALIGN=MIDDLE  ALT=\"2y=48-18=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15 ALIGN=MIDDLE  ALT=\"y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "According to this equation, the length of the longer side is 15 cm.<BR>\n" );
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document.write( "Now we side to check our work. The perimeter is 48 cm.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B9%2B15%2B15=48 ALIGN=MIDDLE  ALT=\"9%2B9%2B15%2B15=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The perimeter checks out. Now we need to check that the ratio of the two sides reduces to 3:5. The ratio 9:15 is equivalent to 3:5 because we can divide both parts by their common factor,3. That is, 9/3=3 sand 15/3=5.<BR>\n" );
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document.write( "Check! So the lengths of the sides of the parallelogram are 9 cm and 15 cm.<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<BR>\n" );
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