document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113459>Question 1113459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wire 10 cm long is cut into two pieces, one of length x and the other of length x and the other of length 10-x. Each piece is bent into a shape of square. Which of the following is the model for the total area enclosed by the two squares of function of x?<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+%28x%5E2-5x%2B50%29%2F8 ALIGN=MIDDLE  ALT=\"A%28x%29=+%28x%5E2-5x%2B50%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+%282x%5E2%2B100%29%2F16 ALIGN=MIDDLE  ALT=\"A%28x%29=+%282x%5E2%2B100%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+%28x%5E2-10x%2B50%29%2F8 ALIGN=MIDDLE  ALT=\"A%28x%29=+%28x%5E2-10x%2B50%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=+%28x%5E2%2B100%29%2F16 ALIGN=MIDDLE  ALT=\"A%28x%29=+%28x%5E2%2B100%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After finding the total area, what is the value of x that minimizes the total area of the two squares? CHOICES(3 cm, 4cm, 5cm, and 6cm) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728496 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=728496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the wires are cut into lengths of x and 10-x.\r<BR>\n" );
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document.write( "they are then shaped into squares.\r<BR>\n" );
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document.write( "the wires form the perimeter of the squares.\r<BR>\n" );
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document.write( "the length of each side of the wire with length x, is equal to x/4.\r<BR>\n" );
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document.write( "the length of each side of the wire with length (10-x) is equal to (10-x) / 4\r<BR>\n" );
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document.write( "the area of each of the squares is equal to s^2, where s is the length of each side of the square.\r<BR>\n" );
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document.write( "the area of the square formed by the wire of length x would be s^2 = (x/4)^2.\r<BR>\n" );
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document.write( "the area of the square formed by the wire of length (10-x), would be s^2 = ((10-x)/4)^2.\r<BR>\n" );
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document.write( "the total area of both square is therefore (x/4)^2 + ((10-x)/4)^2\r<BR>\n" );
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document.write( "since (a/b)^2 is equal to a^2/b^2, the total area therefore becomes equal to x^2/4^2 + (10-x)^2/4^2\r<BR>\n" );
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document.write( "that simplifies to x^2/16 + (10-x)^2/16\r<BR>\n" );
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document.write( "that simplifies to (x^2 + (10-x)^2) / 16\r<BR>\n" );
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document.write( "(10 - x)^2 is equal to (10 - x) * (10 - x) which is equal to 10*10 -10x - 10x + x^2)\r<BR>\n" );
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document.write( "that simplifies to 100 - 20x + x^2.\r<BR>\n" );
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document.write( "therefore (x^2 + (10-x)^2) / 16 becomes (x^2 + 100 - 20x + x^2)/ 16.\r<BR>\n" );
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document.write( "that simplifies to (2x^2 - 20x + 100) / 16\r<BR>\n" );
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document.write( "that simplifies to (x^2 - 10x + 50) / 8\r<BR>\n" );
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document.write( "that looks like selection C.\r<BR>\n" );
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document.write( "you can confirm by assigning an arbitrary value to x that is within the limits of the problem.\r<BR>\n" );
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document.write( "the total length of the wire is 10.<BR>\n" );
document.write( "if you assume that x = 8, then you have lengths of 8 and 2.<BR>\n" );
document.write( "the wires are then formed into 2 squares.<BR>\n" );
document.write( "the first square has a side length of 8/4 = 2<BR>\n" );
document.write( "the second square has a side length of 2/4 = .5<BR>\n" );
document.write( "the area of the first square is 2^2 and the area of the second square is .5^2.<BR>\n" );
document.write( "2^2 + .5^2 = 4 + .25 which is equal to a total area of 4.25.\r<BR>\n" );
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document.write( "using the final formula of (x^2 - 10x + 50) / 8, and replacing x with 8, we get (8^2 - 10*8 + 50) / 8 becomes (64 - 80 + 50) / 8 which becomes 34/8 which becomes 4.25.\r<BR>\n" );
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document.write( "selection C looks good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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