document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061894>Question 1061894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?\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 #676654 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area of rectangle = 2S * S = 2S^2<BR>\n" );
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document.write( "Altitude of the equilateral triangle = square root ( S^2 - S^2/4) = (S/2) * square root(3)<BR>\n" );
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document.write( "Area of equilateral triangle = (1/2) * S * (S/2) * square root(3) = (S^2/4) * square root (3)<BR>\n" );
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document.write( "S^2 - (S^2/4) * square root (3) = S^2 (1 - (square root (3) / 4)) = 0.567S^2<BR>\n" );
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document.write( "Note we use the area of the square, S^2<BR>\n" );
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document.write( "0.567S^2 is area uncovered, then<BR>\n" );
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document.write( "ratio of area uncovered to area of rectangle = 0.567S^2 / 2S^2 = 0.2835<BR>\n" );
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document.write( "0.28 is the fraction of the rectangle's area that is uncovered<BR>\n" );
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