document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=229970>Question 229970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wire 10 cm long is cut into 2 pieces, one of length x and the other of length 10-x. Each piece is bent into the shape of a square.<BR>\n" );
document.write( "a) Find a function that models the total area enclosed by the two squares. <BR>\n" );
document.write( "Would the function be A(x)=-(x+5)²+25?\r<BR>\n" );
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document.write( "b) Find the value of x that minimizes the total area of two squares.<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 #170393 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=170393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A wire 10 cm long is cut into 2 pieces, one of length x and the other of length 10-x. Each piece is bent into the shape of a square.<BR>\n" );
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document.write( "If total length is \"x\", each side of the square is x/4<BR>\n" );
document.write( "and the area is (x/4)^2 <BR>\n" );
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document.write( "If total length is \"10-x\", each side of the square is (10-x)/4<BR>\n" );
document.write( "and the area is [(10-x)/4]^2<BR>\n" );
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document.write( "a) Find a function that models the total area enclosed by the two squares. <BR>\n" );
document.write( "Total Area = (x/4)^2 + [(10-x)/4]^2<BR>\n" );
document.write( "TA = (x^2/16) + [(100 -20x + x^2)/16]<BR>\n" );
document.write( "TA = (1/8)x^2 -(5/4)x + (25/4) <BR>\n" );
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document.write( "b) Find the value of x that minimizes the total area of two squares.<BR>\n" );
document.write( "Min occurs when x = -b/2a = (5/4)/[2(1/8)] = (5/4)/(1/4) = 5<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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