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) (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
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