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Math Help - Optimization calc help. Minimize the perimeter.

  1. #1
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    Optimization calc help. Minimize the perimeter.

    ( I realize that I posted this earlier, the one I posted earlier i left part of the problem out and then the Gentlemen attempting to help my never responded)
    Consider a window the shape of which is a rectangle of height surmounted a triangle having a height that is 1.5 times the width of the rectangle. If the cross sectional area is A, determine the dimensions of the window which minimize the perimeter.



    I think over all area will equal

    A=w*h+1/2(w*h)

    For the rectangle
    A=w*h (obviously)
    Perimeter = 2w+2h

    Triangle
    A=1/2w*t
    Then i turned the triangle into a right triangle by cutting it in half.
    and then to solve for the triangle side we have
    z^2=(x/2)^2+t^2

    I am not sure where to go from here
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  2. #2
    MHF Contributor Calculus26's Avatar
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    A = wh + 1/2wT = wh +1/2w(3w/2) = wh + (3w^2)/4

    P = 2h + w + (10)^1/2w

    since for the side of the triangle s ---- s^2 = (w^2)/4 + T^2


    =(w^2)/4 + (3w/2)^2


    = (w^2)/4 +9(w^2)/4
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