SOLUTION: a painting measuring 12 inches by 18 inches is surrounded by a frame of uniform width. if the combined area of the painting and the frame is 432 square inches, determine the width

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Question 611936: a painting measuring 12 inches by 18 inches is surrounded by a frame of uniform width. if the combined area of the painting and the frame is 432 square inches, determine the width of the frame

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
a painting measuring 12 inches by 18 inches is surrounded by a frame of uniform width. if the combined area of the painting and the frame is 432 square inches, determine the width of the frame
.
Let w = width of frame
then
(12+2w)(18+2w) = 432
216+24w+36w+4w^2 = 432
216+60w+4w^2 = 432
4w^2+60w+216 = 432
4w^2+60w-216 = 0
w^2+15w-54 = 0
(w+18)(w-3) = 0
w = {-18,3}
throw out the negative solution (extraneous) leaving:
w = 3 inches