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Math Help - express the perimeter of triangle P as function of area A

  1. #1
    Member sluggerbroth's Avatar
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    express the perimeter of triangle P as function of area A

    express the perimeter of triangle P as function of area A
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  2. #2
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    Re: express the perimeter of triangle P as function of area A

    This is impossible. All triangles with vertices at (n, 0), (-n, 0) and (0, 1/n) have area 1.
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    Re: express the perimeter of triangle P as function of area A

    Hello, sluggerbroth!

    Who asked this question? . . . It is stupid!


    Express the perimeter of triangle P as function of area A.
    Code:
        - - - - * - - - - - - - - - - - - * - - - - - - - - - - - - * -
        :      * *                      * *                      * *  :
        :     *   *                   *   *                   *   *   :
        3    *     *                *     *                *     *    3
        :   *       *             *       *             *       *     :
        :  *         *          *         *          *         *      :
        - *  *  *  *  * - - - *  *  *  *  * - - - *  *  *  *  * - - - -
          : - - 4 - - :       : - - 4 - - :       : - - 4 - - :
    All these triangles have an area of 6 square units.

    But obviously they have different perimeters.


    So P \:=\:f(6)\, has at least three possible values.
    . . It is not a function.
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    Re: express the perimeter of triangle P as function of area A

    How about P=a+b+c and A=\rho \cdot s where \rho is the radius of the inscribed circle, and s=\frac{a+b+c}{2}=\frac{P}{2}. Now P=\frac{2 A}{\rho}. This can be considered a function in A (not just A, but A nevertheless).
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  5. #5
    Member sluggerbroth's Avatar
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    Re: express the perimeter of triangle P as function of area A

    This comes from Schaumís Outlines Precalculus
    It is a two part question and reads as follows:
    A) Express the area A of equilateral triangle as function of one side s.
    B) Express the perimeter of the triangle P as a function of the area A.

    The answers listed are:
    A) A(s)=(s squared )(square root 3)/4
    and
    B) P(A)=(6 square root A)/ (fourth root 3)

    How to get to these answers???? HELP!!
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    Re: express the perimeter of triangle P as function of area A

    Quote Originally Posted by sluggerbroth View Post
    A) Express the area A of equilateral triangle as function of one side s.
    You mislead people in this thread by omitting the word "equilateral." To answer this question, draw an altitude, which is also a median, and use the Pythagorean theorem to find its length.
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  7. #7
    Member sluggerbroth's Avatar
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    Re: express the perimeter of triangle P as function of area A

    I got part a of this but not part b B) Express the perimeter of the triangle P as a function of the area A.

    How to get to this answer???? HELP!!
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  8. #8
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    Re: express the perimeter of triangle P as function of area A

    Quote Originally Posted by sluggerbroth View Post
    I got part a of this but not part b B) Express the perimeter of the triangle P as a function of the area A.
    So, P = 3s and you cannot express s through A from the equation A=\frac{s^2\sqrt{3}}{4}? Multiply both sides by 4/\sqrt{3} and takes the square root of both sides.
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