A matte of uniform width is to be placed around a painting so that the area of the matted surface is equal to the area of the painting. If the dimensions of the painting are 15 cm and 10 cm, find the width of the matte. The answer is supposed to be 2.5 cm but I keep getting 12.5.

Answer 1

subtract the area of the painting from the total area. If the matte has width w, then

(10+2w)(15+2w) - 10*15 = 10*15
4w^2 + 50w - 150 = 0
2(2w-5)(w+15) = 0
w = 5/2 = 2.5