Question:
If the volume of a cuboid is \[ 3x^2-27, \] then its possible dimensions are
(a) \[ 3,\ x^2,\ -27x \]
(b) \[ 3,\ x-3,\ x+3 \]
(c) \[ 3,\ x^2,\ 27x \]
(d) 3, 3, 3
Solution:
Volume of cuboid = Length × Breadth × Height
Given:
\[ 3x^2-27 \]
Taking 3 common:
\[ =3(x^2-9) \]
Using identity:
\[ a^2-b^2=(a-b)(a+b) \]
\[ =3(x-3)(x+3) \]
Therefore, the possible dimensions are:
\[ 3,\ x-3,\ x+3 \]
Hence, the correct answer is:
\[ \boxed{3,\ x-3,\ x+3} \]