Question

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? Volume : $3x^2-12x$

Answer 1

Step 1. Factorize the given expression of volume.

$$\begin{gathered} \Rightarrow V=3x^2-12x \\ \Rightarrow V=3x(x-4) \\ \Rightarrow V=3\times x\times (x-4) \end{gathered}$$

Step 2. Find possible dimensions of the cuboid.

The volume of the cuboid is computed by using the formula,

$V=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}$

Compare the above equation with $V=3\times x\times (x-4)$

Hence the dimension of the cuboid are $3,x\mathrm{and}(x-4)$

Hence, the possible expression for the dimension of the cuboid are,

$\mathbf{3}\mathbf{,}\mathbf{}\mathit{x}\mathbf{}\mathbf{and}\mathbf{}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{4}\mathbf{)}$