A picture is four inches wide and six inches long. It has an additional border of uniform width. If the area of the picture is equal to the area of the border, what is the width of the border?

Answer 1

(4+2w)(6+2w) = 2*24 = 48

24 + 20 w + 4 w^2 = 48

4 w^2 + 20 w - 24 = 0

w^2 + 5 w - 6 = 0
(w+6)(w-1) = 0
w = 1
check
4+2 = 6
6+2 = 8
6*8 = 48
48 - 24 = 24 yes