document.write( "Question 404474: A wire L = 16 cm long is cut into two pieces, one of length x and the other of length (L - x). Each piece is bent into the shape of a square.\r
\n" ); document.write( "\n" ); document.write( "(a) Find a function that models the total area A enclosed by the two squares in terms of x.
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\n" ); document.write( "\n" ); document.write( "(b) Find the value of x that minimizes the total area of the two squares.
\n" ); document.write( "x = ____ cm \n" ); document.write( "

Algebra.Com's Answer #285890 by richard1234(7193) $\"\"$ $\"About$

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Since the perimeters of the two squares are x and L-x respectively, then the side lengths are $\"x%2F4\"$ and $\"%28L-x%29%2F4\"$ . The sums of the two areas are:\r
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\n" ); document.write( "\n" ); document.write( "The minimum occurs when $\"A%28x%29\"$ is minimized, which also happens when $\"2x%5E2+-+2Lx+%2B+L%5E2\"$ is minimized. Either using the vertex of the parabola or by differentiating, we obtain $\"x+=+-%28-2L%29%2F4+=+L%2F2\"$ , so the minimum area occurs when the wire is cut into two pieces of 8 cm. \n" ); document.write( "

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