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.

Question

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

Answer 1

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!