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Math Help - Maximum & Minimum Problems

  1. #1
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    Maximum & Minimum Problems

    I am having some issues with these problems.
    1. A farmer constructing a rectangluar fenced area with 420 meters of fencing. Calculate the dimensions that will yield the maximum area?

    2. The sum of the base and height measures of a triangle is 15cm. What base height will generate the maximum area of the triangle?

    I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.
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  2. #2
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    Quote Originally Posted by Kat.T View Post
    I am having some issues with these problems.
    1. A farmer constructing a rectangluar fenced area with 420 meters of fencing. Calculate the dimensions that will yield the maximum area?

    I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.
    Perimeter = 420 = 2x + 2y. Therefore y = 210 - x.

    Area = xy = x (210 - x).

    A = x(210 - x) is a parabola. Use what you've been taught to find it's turning point.

    Quote Originally Posted by Kat.T View Post
    2. The sum of the base and height measures of a triangle is 15cm. What base height will generate the maximum area of the triangle?

    I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.
    b + h = 15 => b = 15 - h.

    A = bh/2 = (15 - h)h/2.

    A = (15 - h)h/2 is a parabola. Use what you've been taught to find it's turning point.
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