document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210520>Question 1210520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A regular hexagon has a perimeter of p (in length units) and an area of A (in square units). If A=3/2 then find the side length of the hexagon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853447 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ```python<BR>\n" );
document.write( "import math\r<BR>\n" );
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document.write( "# A = (3 * sqrt(3) / 2) * s^2<BR>\n" );
document.write( "# 3/2 = (3 * sqrt(3) / 2) * s^2<BR>\n" );
document.write( "# 1 = sqrt(3) * s^2<BR>\n" );
document.write( "# s^2 = 1 / sqrt(3)<BR>\n" );
document.write( "# s = 1 / (3**(1/4))\r<BR>\n" );
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document.write( "s = 1 / (3**0.25)<BR>\n" );
document.write( "print(f\"s = {s}\")<BR>\n" );
document.write( "print(f\"s^4 = {s**4}\")<BR>\n" );
document.write( "print(f\"1/3 = {1/3}\")\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "```text<BR>\n" );
document.write( "s = 0.7598356856515925<BR>\n" );
document.write( "s^4 = 0.3333333333333333<BR>\n" );
document.write( "1/3 = 0.3333333333333333\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "To find the side length of a regular hexagon given its area, we use the standard area formula for a regular hexagon with side length .\r<BR>\n" );
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document.write( "### 1. The Area Formula\r<BR>\n" );
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document.write( "A regular hexagon can be divided into six equilateral triangles. The area of one equilateral triangle with side  is . Therefore, the total area  of the hexagon is:\r<BR>\n" );
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document.write( "### 2. Solving for the Side Length ()\r<BR>\n" );
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document.write( "We are given that the area . Substituting this into the formula:\r<BR>\n" );
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document.write( "To solve for , we divide both sides by :\r<BR>\n" );
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document.write( "Now, we take the square root of both sides to find :\r<BR>\n" );
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document.write( "Using exponent notation,  and . Thus:\r<BR>\n" );
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document.write( "### Summary\r<BR>\n" );
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document.write( "If the area  is exactly , the side length of the hexagon is:\r<BR>\n" );
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document.write( "*(Note: In many geometry problems, the area is given as . In that specific case, the side length would simplify to exactly ****. However, based on the value  provided, the side length is .)* </SPAN>\n" );
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