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A large painting in the style of Rubens is 3 feet longer than it is wide. If the wooden frame is 18 in wide and the area of the picture frame is 286 ft^2, find the dimensions of the painting.

I have the basic idea down of what I'm supposed to do to solve it.. But I just can't put it all together in my head. Helpppp

  • Pre-Calc -

    Always draw a diagram, then use what info you have been given.

    width = w
    length = w+3

    Since the frame is 1.5' wide, the total width and length get increased by 3 ft for the entire framed picture.

    picture area: width*length = w(w+3)
    total framed area: (width+3)(length+3) = (w+3)(w+6)

    The total area less the area of the picture is the area of the frame:

    (w+3)(w+6) - w(w+3) = 286
    w^2 + 9w + 18 - w^2 - 3w = 286
    6w + 18 = 286
    6w = 268
    w = 44' 8"

    wow! Big painting!

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