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Calc

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A wire 100 inches long is to be cut into two pieces. One of the pieces will be bent into the shape of a circle and the other into the shape of a equilateral triangle. How should the wire be cut so as to maximize the sum of the area of the areas of the circle and triangle will be maximized?

  • Calc - ,

    L=total length,
    x=length of piece for triangle

    So
    L-x=circumference of circle
    At(x)=area of triangle
    =√3 *x²/4
    Ac(x)=area of circle
    =π((L-x)/(2π))²
    =(L-x)²/(4π)

    Total Area, A(x)
    = At(x)+Ac(x)
    To find the maximum/minimum,
    Equate
    A'(x)=0 and solve for x.
    Find A(x) = max. area.

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