document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288606>Question 288606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square and an equilateral triangle both have area of 16&#8730;3.Find the ratio of the length of the square side to the length of the triangle side. (Round your answer to the nearest hundredth)\r<BR>\n" );
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document.write( "A) 0.25 B) 0.66 C) 1.52 D) 4 E) none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209189 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=209189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square and an equilateral triangle both have area of 16&#8730;3.Find the ratio of the length of the square side to the length of the triangle side. (Round your answer to the nearest hundredth) <BR>\n" );
document.write( "A) 0.25 B) 0.66 C) 1.52 D) 4 E) none of these\r<BR>\n" );
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document.write( "Let x be a side of the square and y be a side of the triangle. Then we have:\r<BR>\n" );
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document.write( "area of the square = x^2 = 16*sqrt(3)\r<BR>\n" );
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document.write( "1.) x = 4*3^(1/4)\r<BR>\n" );
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document.write( "area of the triangle = 1/2*base*height\r<BR>\n" );
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document.write( "Let h be the altitute of the equalateral triangle. The altitute forms two right triangles. By the Pythagorean Theorem we have then:\r<BR>\n" );
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document.write( "y^2 = (y/2)^2 + h^2 \r<BR>\n" );
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document.write( "h^2 = y^2 - (y/2)^2<BR>\n" );
document.write( "h^2 = (3/4)*y^2\r<BR>\n" );
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document.write( "The area of the triangle then is:\r<BR>\n" );
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document.write( "(1/2)*y*(3/4)*y^2) = 16*sqrt(3)\r<BR>\n" );
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document.write( "(3/8)*y^3 = 16*sqrt(3)<BR>\n" );
document.write( "y^3 = (8/3)*16*sqrt(3)<BR>\n" );
document.write( "2.) y^3 = (128/3)*sqrt(3)\r<BR>\n" );
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document.write( "Note that x/y = x^3/y^3.\r<BR>\n" );
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document.write( "From 1.) we have x^3 = (4*3^1/4)^3\r<BR>\n" );
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document.write( "x/y = x^3/y^3 = (64*(3^(3/4))/((128/3)*sqrt(3))\r<BR>\n" );
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document.write( " </SPAN>\n" );
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