Let us assume side length of a square sign = x feet.
Side of the square poster is 2 feet less than the sides of a square sign.
Therefore, side of the square poster in terms of x is = (x-2) feet.
Given the difference between their areas is 40 square feet.
We know, area of a square = (side)^2.
Therefore, we can setup an equation,
(Square sign side length)^2 - ( square poster side length)^2 = 40.
(x)^2 - (x-2)^2 = 40.
Expanding (x-2)^2 = x^2 +(2)^2 -2(x)(2) = x^2 + 4 - 4x, we get
x^2- (x^2 + 4 - 4x ) = 40.
Distributing minus sign over parenthesis, we get
x^2 -x^2 -4 +4x =40.
Combining like terms, x^2-x^2=0, we get
0-4+4x=40.
-4 +4x =40.
Adding 4 on both sides, we get
-4 +4 +4x =40+4.
4x = 44.
Dividing both sides by 4.
4x/4 = 44/4.
x= 11.
Therefore, side length of a square sign = 11 feet.
The square poster is 2 feet less than the sides of a square sign.
2 less than 11 is 11-2 = 9 feet.
Therefore, the square poster is 9 feet.