Answers:
The sign is 4 ft on a side
The poster is 2 ft on a side
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Explanation:
s = side length of the sign
p = side length of the poster
The poster "has sides measuring 2 ft less than the sides of the square sign", so p = s-2. Whatever the value of 's' is, we subtract off 2 to get the value of p. For example, if the sign has side lengths of s = 10 ft, then p = s-2 = 10-2 = 8 ft is the side length of the poster
We don't know s or p right now, so they are simply placeholders for some numbers.
If s is the side length of the sign, then s*s = s^2 is the area
If p is the side length of the poster, then p*p = p^2 is the area of the poster. We can replace p with s-2 since p = s-2. So we end up with p^2 = (s-2)^2 = s^2 - 4s + 4 after using the FOIL rule
Now subtract the two areas and set that difference equal to 12. Solve for s
(area of sign) - (area of poster) = 12
(s^2) - (s^2 - 4s + 4) = 12
s^2 - s^2 + 4s - 4 = 12
4s - 4 = 12
4s - 4+4 = 12+4
4s = 16
4s/4 = 16/4
s = 4
The sign's side length is 4, so its area is 4^2 = 16
If s = 4, then p is
p = s-2
p = 4-2
p = 2
The poster's side length is 2, so its area is 2^2 = 4
Subtract the areas: 16 - 4 = 12
The answer is confirmed
