document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253415>Question 253415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. If the perimeter of a rectangle is 8&#8730;2 cm, what is the smallest possible value of the length of one of its diagonals in cm?\r<BR>\n" );
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document.write( "I've tried:<BR>\n" );
document.write( "let length be l, width be w, and diagonal be d<BR>\n" );
document.write( "let l be x, then w will be:<BR>\n" );
document.write( "(8&#8730;2-2x)/2 = 4&#8730;2-x\r<BR>\n" );
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document.write( "d^2=l^2+w^2<BR>\n" );
document.write( "      =x^2+(4&#8730;2-x)^2<BR>\n" );
document.write( "      =x^2+(32-8&#8730;2x-x^2)<BR>\n" );
document.write( "      =32-8&#8730;2x... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185689 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let length be l, width be w, and diagonal be d<BR>\n" );
document.write( "let l be x, then w will be:<BR>\n" );
document.write( "(8&#8730;2-2x)/2 = 4&#8730;2-x <BR>\n" );
document.write( "d^2=l^2+w^2<BR>\n" );
document.write( "=x^2+(4&#8730;2-x)^2<BR>\n" );
document.write( "=x^2+(32-8&#8730;2x-x^2) ___ not quite ___ the x^2 in the expansion is positive (negative times negative is positive)<BR>\n" );
document.write( "=32-8&#8730;2x... ___ 2x^2 - 8&#8730;2x + 32\r<BR>\n" );
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document.write( "this is a quadratic (parabola) with a minimum on the axis of symmetry\r<BR>\n" );
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document.write( "x = -b / 2a = 8&#8730;2 / 4 = 2&#8730;2\r<BR>\n" );
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document.write( "substituting ___ d^2 = 2(2&#8730;2)^2 - 8&#8730;2(2&#8730;2) + 32 = 16 - 32 + 32 = 16\r<BR>\n" );
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document.write( "d = 4 </SPAN>\n" );
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