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Math Help - Find Perimeter

  1. #1
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    Find Perimeter

    If the area of a square is 9x^2 - 12xy + 4y^2, what is the perimeter of the square?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    If the area of a square is 9x^2 - 12xy + 4y^2, what is the perimeter of the square?
    Hi magentarita,

    9x^2-12xy+4y^2 can be factored into (3x-2y)^2

    Now we know that the area of a square is s^2, where s is one side.

    That means that s=3x-2y

    We have 4 of them, so P=4(3x-2y)=12x-8y
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  3. #3
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    Hi

    9x^2 - 12xy + 4y^2 = (3x-2y)^2

    Therefore the length of the sides is 3x-2y (or 2y-3x depending by the the sign of this quantity)

    The perimeter is four times the length
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  4. #4
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    Tell me...

    Quote Originally Posted by masters View Post
    Hi magentarita,

    9x^2-12xy+4y^2 can be factored into (3x-2y)^2

    Now we know that the area of a square is s^2, where s is one side.

    That means that s=3x-2y

    We have 4 of them, so P=4(3x-2y)=12x-8y
    How do you factor this polynomial?
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by masters View Post
    Hi magentarita,

    9x^2-12xy+4y^2 can be factored into (3x-2y)^2

    9x^2 - 12xy + 4y^2

    = (3x)^2 - 6xy-6xy +(2y)^2


    =3x(3x-2y) - 2y(3x-2y)<br />

    =(3x-2y)(3x-2y) = (3x-2y)^2

    ----------------------

    You should remember the formula that

    a^2 - 2ab +b^2 = (a-b)^2

    Here a = 3x & b= 2y
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  6. #6
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    Talking

    Quote Originally Posted by magentarita View Post
    How do you factor this polynomial?
    To learn how to factor quadratics, try some online lessons. :wink:
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  7. #7
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    thanks

    Quote Originally Posted by ADARSH View Post
    9x^2 - 12xy + 4y^2

    = (3x)^2 - 6xy-6xy +(2y)^2


    =3x(3x-2y) - 2y(3x-2y)<br />

    =(3x-2y)(3x-2y) = (3x-2y)^2

    ----------------------
    You should remember the formula that

    a^2 - 2ab +b^2 = (a-b)^2

    Here a = 3x & b= 2y
    Thank you for breaking down this question.
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