document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906830>Question 906830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a rectangles diagonal is 32 inch what will be its length<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 #550085 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you don't have enough information to determine this exactly.\r<BR>\n" );
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document.write( "the diagonal of a rectangle is equal to 32.\r<BR>\n" );
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document.write( "by the pythagorean formula, the diagonal squared of the rectangle is equal to its length squared plus its width squared.\r<BR>\n" );
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document.write( "solve for it's length and you get it's length is equal to the square root of (it's length squared minus its width squared).\r<BR>\n" );
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document.write( "in algebraic terms, this looks like L^2 = (32^2 - W^2)\r<BR>\n" );
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document.write( "you can pretty much pick any W^2 that is less than 32^2 and you will get a corresponding length that will satisfy the equation.\r<BR>\n" );
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document.write( "assuming W^2 = 31^2, you will find a corresponding L^2 that is equal to 63.\r<BR>\n" );
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document.write( "if L^2 is equal to 63, then L is equal to sqrt(63)\r<BR>\n" );
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document.write( "you have a length of sqrt(63) and a width of 31 and a diagonal of 32.\r<BR>\n" );
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document.write( "31^2 + sqrt(63)^2 = 32^2 becomes 961 + 63 = 1024 which becomes 1024 = 1024 which confirms that the solution of L^2 = 63 is correct.\r<BR>\n" );
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document.write( "pick any other value of W^2 less than 32^2 and you'll get another value of L that will satisfy the equation.\r<BR>\n" );
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document.write( "now if you're talking about a square rather than a rectangle, then you can solve for the length of a side because length and width are now the same measure.\r<BR>\n" );
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document.write( "in that case you get s^2 + s^2 = 32^2 which becomes 2s^2 = 32^2 which gets you s^2 = 512 which gets you s = sqrt(512), s being the length of a side of the square.\r<BR>\n" );
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