document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33408>Question 33408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The apothem of a regular polygon is the perpendicular distance from the center of the polygon to a side. The area, A, of a regular polygon varies jointly as the apothem, a, and the perimeter,p. A regular triangle with an apothem of 3 inches and a perimeter of 31.2 inches has an area of 46.8 square inches.\r<BR>\n" );
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document.write( "Find the constant variation<BR>\n" );
document.write( "Write a joint variation equation<BR>\n" );
document.write( "Find the area of a regular triangle with an apothem of 2.3 inches and a perimeter of 12 inches.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19859 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=19859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, you can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28k%29%28a%29%28p%29 ALIGN=MIDDLE  ALT=\"A+=+%28k%29%28a%29%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the value of k, the constant of variation, substitute the given values of A, a, and p.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.8+=+%28k%29%283%29%2831.2%29 ALIGN=MIDDLE  ALT=\"46.8+=+%28k%29%283%29%2831.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.8+=+93.6%28k%29 ALIGN=MIDDLE  ALT=\"46.8+=+93.6%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 93.6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.8%2F93.6+=+k ALIGN=MIDDLE  ALT=\"46.8%2F93.6+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0.5 ALIGN=MIDDLE  ALT=\"k+=+0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Constant of variation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+0.5ap ALIGN=MIDDLE  ALT=\"A+=+0.5ap\"   DISABLED_style= \"max-width:90%; height:auto;\" > Joint variation equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+0.5%282.3%29%2812%29 ALIGN=MIDDLE  ALT=\"A+=+0.5%282.3%29%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+13.8 ALIGN=MIDDLE  ALT=\"A+=+13.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >sq.ins.\r<BR>\n" );
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document.write( "There is a problem with answer!<BR>\n" );
document.write( "If you calculate the area of the given regular (equilateral) triangle using Heron's formula<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you will get 6.9 sq.ins. which is just half of what I got using the direct variation method above.\r<BR>\n" );
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document.write( "I have concluded that the given apothem (a = 2.3 inches) is just twice what it should be for a regular triangle of 4 inches per side.\r<BR>\n" );
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document.write( "You might want to check this out.\r<BR>\n" );
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