The answer is 16x + 12.
The volume of a prism is:
V = l w h
l - length, w - width, h - height
144x³ + 216x² + 81x = l w h
9x 16x² + 9x 24x + 9x 9 = l w h
9x(16x² + 24x + 9) = l w h
9x((4x)² + 2 4x 3 + 3²) = l w h
9x(4x + 3)² = l w h
9x(4x + 3)(4x + 3) = l w h
So, one side is 9x, other is 4x + 3 and another is 4x + 3.
Square face will have both sides the same, so its sides are 4x + 3. Perimeter of a square is 4 times its side:
P = 4 (4x + 3) = 4 4x + 4 3 = 16x + 12
