document.write( "Question 928247: Bob wants to cut a wire that is 60 cm long into two pieces. Then he wants to make each piece into a square. Determine how the wire should be cut so that the total area of the two squares is as small as possible. \n" ); document.write( "

Algebra.Com's Answer #563579 by KMST(5328) $\"\"$ $\"About$

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Let $\"x\"$ be the length of one of the pieces, in cm.
\n" ); document.write( " $\"60-x\"$ = the length of the other piece, in cm.
\n" ); document.write( "The sides of the squares made will measure $\"x%2F4\"$ and $\"%2860-x%29%2F4\"$ cm,
\n" ); document.write( "and the areas of those squares, in square cm, will be
\n" ); document.write( " $\"%28x%2F4%29%5E2=x%5E2%2F16\"$ and $\"%28%2860-x%29%2F4%29%5E2=%283600-120x%2Bx%5E2%29%2F16\"$ respectively.
\n" ); document.write( "The total area of ththe two squares, in square cm, will be
\n" ); document.write( "

\n" ); document.write( "That expression, like $\"x%5E2-60x%2B1800\"$ is a quadratic function of $\"x\"$ .
\n" ); document.write( "Quadratic functions have the general form $\"f%28x%29=ax%5E2%2Bbx%2Bc\"$ ,
\n" ); document.write( "and if $\"a%3E0\"$ the quadratic function has a minimum at $\"x=-b%2F2a\"$ .
\n" ); document.write( "Both, $\"%28x%5E2-60x%2B1800%29%2F8\"$ and $\"x%5E2-60x%2B1800\"$ , have a minimum at
\n" ); document.write( " $\"x=-%28-60%29%2F2\"$ --> $\"x=30\"$ .
\n" ); document.write( "So, to make the total area of the two squares is as small as possible, the wire should be cut in half, making two 30-cm pieces. \n" ); document.write( "

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