Answer:
8 inches
Explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.