document.write( "Question 334785: A piece of wire 60cm in length is cut and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square.
\n" ); document.write( "I know to solve this you need to make an equation in which the X (the amount of wire for a square) is a function of the Total area, but stuck \n" ); document.write( "

Algebra.Com's Answer #239883 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Circumference of circle + Perimeter of Square = 60\r\n" );
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document.write( "Solve for r\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "Multiply both sides by \r\n" );
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document.write( "Let y = Area of circle + Area of square\r\n" );
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document.write( "We need to substitute for \r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "[If you were taking calculus you would take the derivative here and set it\r\n" );
document.write( "equal to 0, but I am assuming that you are taking college algebra, so you must\r\n" );
document.write( "use the vertex formula.]\r\n" );
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document.write( "or in descending powers:\r\n" );
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document.write( "The coefficient of  is positive so this represents\r\n" );
document.write( "a parabola that opens upward, so its vertex will be at a minimum\r\n" );
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document.write( "To find the x-cordinate of the vertex, we use the vertex formula\r\n" );
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document.write( "x-coordinate of vertex = \r\n" );
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document.write( "x-coordinate of vertex = \r\n" );
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document.write( "So for the minimum area, the side of a square will be  cm.\r\n" );
document.write( "That is approximately 8.401487303 cm.\r\n" );
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document.write( "We will need to cut the wire at 4 times the side of the square.\r\n" );
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document.write( "So we must cut the wire at  or  \r\n" );
document.write( "or about 33.60594921 cm from one end and, subtracting from 60,\r\n" );
document.write( "26.39405079 cm from the other end.\r\n" );
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document.write( "Now for the maximum area. The problem is only defined for \r\n" );
document.write( "When x=0, the square shrinks to 0 and the whole 60cm wire is made into a\r\n" );
document.write( "circle.  When x=15, making the perimeter of the square 60 cm, the circle\r\n" );
document.write( "shrinks to 0 and the whole 60cm wire is made into a square.  Since the parabola\r\n" );
document.write( "opens upward, the maximum value is at one endpoint of the interval, either when\r\n" );
document.write( "x=0 or when x=15.  It is well known that if a piece of wire is bent into a\r\n" );
document.write( "circle or a square, the circle will have more area, so we could just assume the\r\n" );
document.write( "maximum area would be when we \"cut\" the wire 0, or no, centimeters from the\r\n" );
document.write( "end, and bend the whole wire into a circle. That is we don't cut the wire at\r\n" );
document.write( "all.\r\n" );
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document.write( "Edwin

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