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math problem

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A simple rain gutter is constructed using a sheet of aluminum that is 40cm wide. The edges are turned up to form right angles. Determine the depth of the gutter that will maximize the cross-sectional area (allowing the greatest amount of water to flow).

I don't know where and how to start.

please help and thank you

  • math problem -

    make a sketch.
    Assuming that the gutter is rectangular and the sides must have the same height, look at the cross section of the gutter.
    let the base by y and each of the sides by x

    we know that
    2x + y = 40
    y = 40-2x

    the area A of the cross-section will be
    A = xy
    = x(40-2x) = 40x - 2x^2
    Assuming this is a typical Calculus question ...

    dA/dx = 40 - 4x = 0 for a max of A
    40-4x = 0
    x = 10
    the the depth will be 10 cm

    if you don't know Calculus , you will have to complete the square on
    A = 40x - 2x^2

  • math problem -

    I don't know calculus

    This is what I got after completing the square:
    A=-2(x-10)^2+200

    How do I know what is the depth when I complete the square?

    thank you

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