A picture 8 inches by 12 inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture, find the width of the frame
Let the width of the frame be = W
So....the area of the picture and frame = (8 + 2W) (12 + 2W)
And this whole area - the area of the picture = the area of the picture.....so....
(8 + 2W) ( 12 + 2W) - 96 = 96
96 + 24W + 16W + 4W^2 - 96 = 96 simplify
4W^2 + 40W - 96 = 0 divide through by 4
W^2 + 10W - 24 = 0 factor
(W + 12) ( W - 2) =0
Setting each factor to 0 and solving for W produces
W = -12 inches [ reject]
or
W = 2 inches [ correct answer ]