document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442490>Question 442490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is it possible without side lenghts, to prove that a rectangle missing one of its long sides is a square?  The diagonals are drawn in.  I think my professor may have left out some critical information, but if she didn't I am totally stuck.\r<BR>\n" );
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document.write( "Thank you,\r<BR>\n" );
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document.write( "Gianni Maiorano </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305211 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s be the short side of your \"rectangle.\" And let l be the long side. Let d be your diagonal.\r<BR>\n" );
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document.write( "Given the pythagorean theorem, your diagonal will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"s%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if your rectangle is indeed a square.\r<BR>\n" );
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document.write( "Use s^2 + l^2 = d^2 to find l^2.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+s%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d+=+s%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then s^2 +l^2 = 2s^2 and thus l^2 = s^2, hence l=s.\r<BR>\n" );
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document.write( "Since your long side and short side are actually the same length, then the rectangle is also a square.\r<BR>\n" );
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document.write( "Does this make sense?\r<BR>\n" );
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document.write( "------- EDIT\r<BR>\n" );
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document.write( "I see your teacher said without side lengths.\r<BR>\n" );
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document.write( "A rectangle can be broken into two triangles.\r<BR>\n" );
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document.write( "If the two sides are the same, then the two corresponding angles will be the same. Namely, they will both be 45º.\r<BR>\n" );
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document.write( "Check the angles formed by the triangle. If one of the angles is 45, then you're set. It would be a square.<BR>\n" );
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