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math

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The area of a frame is equal to 120in^2.it surrounds a 4in x 6in photo.the frame is of uniform width.how wide is the frame ?

  • math -

    the 4x6 photo has area 24 in^2
    So, the frame has area 120-24 = 96 in^2

    If the frame has width x, then its area is

    2(4x) along the ends
    +2(6x) along the sides
    +4x^2 on the corners

    so,

    4x^2 + 8x + 12x = 96
    x^2 + 5x - 24 = 0
    x = 3

    So, the frame is 3in wide

    check:
    total dimensions are 10x12, so area = 120

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