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Alg 2

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a rectangular picture frame measures 8 inches by 4 inches. You want to triple the frame's area by adding the same distance, x, to the length and width.
Find the value of x and find the new dimensions of the frame.

How do you do this?? Please show work

  • Alg 2 -

    L = Lenght = 8 in

    W = Width = 4 in

    A = Area = L*W = 8*4 = 32 in^2

    3A = 3*32 = 96 in^2

    (L+x)*(W+x) = 3A

    (8+x)*(4+x) = 96

    4*8 + 4*x + x*8 + x*x = 96

    32 + 4x + 8x + x^2 = 96

    x^2 + 12x + 32 - 96 = 0

    x^2 + 12x - 64 = 0

    The exact solutions of this equation are:

    x = 4

    and

    x = -16

    Distance can't be negative so:

    x=4

    (8+4) * (4+4) = 12 * 8 = 96 in^2 = 3A

  • Alg 2 -

    The new dimensions of the frame are:

    Lenght = 8+4 = 12 in

    Width = 4+4 = 8 in

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