Answer:
x² + 12x - 160 = 0
x = 8 or x = -20
The dimensions are 2 cm, 11 cm, 17 cm.
Explanation:
The volume of the cuboid is the product of the three dimensions.
volume = 2(x + 3)(x + 9)
volume = 2(x² + 12x + 27)
volume = 2x² + 24x + 54
We are told the volume equals 374 cm³.
2x² + 24x + 54 = 374
2x² + 24x - 320 = 0
x² + 12x - 160 = 0
(x - 8)(x + 20) = 0
x - 8 = 0 or x + 20 = 0
x = 8 or x = -20
We do not use x = -20 because it would cause two dimensions to be negative which cannot be.
x = 8
x + 3 = 8 + 3 = 11
x + 9 = 8 + 9 = 17
The dimensions are 2 cm, 11 cm, 17 cm.